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Journal articles on the topic 'Constrained quantum mechanics'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

MARANER, P., and C. DESTRI. "GEOMETRY-INDUCED YANG-MILLS FIELDS IN CONSTRAINED QUANTUM MECHANICS." Modern Physics Letters A 08, no. 09 (March 21, 1993): 861–68. http://dx.doi.org/10.1142/s0217732393000891.

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We derive the effective Hamiltonian for a quantomechanical system constrained to move on a submanifold M of its configuration space Rn by a confining potential V. Besides potential terms proportional to the intrinsic and mean curvature of M the restriction to the constraint produce the minimal interaction with a geometry-induced Yang-Mills field.

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2

SHABANOV, SERGEI V. "q-OSCILLATORS, NON-KÄHLER MANIFOLDS AND CONSTRAINED DYNAMICS." Modern Physics Letters A 10, no. 12 (April 20, 1995): 941–48. http://dx.doi.org/10.1142/s0217732395001034.

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It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kähler manifolds, or as a quantum theory with second- (or first-) class constraints.

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3

Elze, Hans-Thomas. "On quantum mechanics as constrained supersymmetric classical dynamics." Physics Letters A 335, no. 4 (February 2005): 258–65. http://dx.doi.org/10.1016/j.physleta.2004.12.045.

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4

Salazar, R., and G. Téllez. "Constrained quantum mechanics: chaos in non-planar billiards." European Journal of Physics 33, no. 4 (May 23, 2012): 965–85. http://dx.doi.org/10.1088/0143-0807/33/4/965.

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5

Deriglazov, A. A. "Quantum mechanics on noncommutative plane and sphere from constrained systems." Physics Letters B 530, no. 1-4 (March 2002): 235–43. http://dx.doi.org/10.1016/s0370-2693(02)01262-5.

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6

Bogusz, A., and A. Gozdz. "The algebraic generator coordinate method as the constrained quantum mechanics." Journal of Physics A: Mathematical and General 25, no. 17 (September 7, 1992): 4613–24. http://dx.doi.org/10.1088/0305-4470/25/17/020.

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7

Tan, De Kun. "Application of Quantum-Behaved Particle Swarm Optimization in Engineering Constrained Optimization Problems." Advanced Materials Research 383-390 (November 2011): 7208–13. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.7208.

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To overcome the shortage of standard Particle Swarm Optimization(SPSO) on premature convergence, Quantum-behaved Particle Swarm Optimization (QPSO) is presented to solve engineering constrained optimization problem. QPSO algorithm is a novel PSO algorithm model in terms of quantum mechanics. The model is based on Delta potential, and we think the particle has the behavior of quanta. Because the particle doesn’t have a certain trajectory, it has more randomicity than the particle which has fixed path in PSO, thus the QPSO more easily escapes from local optima, and has more capability to seek the global optimal solution. In the period of iterative optimization, outside point method is used to deal with those particles that violate the constraints. Furthermore, compared with other intelligent algorithms, the QPSO is verified by two instances of engineering constrained optimization, experimental results indicate that the algorithm performs better in terms of accuracy and robustness.

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8

Bernard, B. J., and L. C. Lew Yan Voon. "Notes on the quantum mechanics of particles constrained to curved surfaces." European Journal of Physics 34, no. 5 (July 26, 2013): 1235–41. http://dx.doi.org/10.1088/0143-0807/34/5/1235.

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9

Hong, Soon-Tae, Joohan Lee, Tae Hoon Lee, and Phillial Oh. "A complete solution of a constrained system: SUSY monopole quantum mechanics." Journal of High Energy Physics 2006, no. 02 (February 15, 2006): 036. http://dx.doi.org/10.1088/1126-6708/2006/02/036.

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10

Doldán, Ricardo, Rodolfo Gambini, and Pablo Mora. "Quantum mechanics for totally constrained dynamical systems and evolving hilbert spaces." International Journal of Theoretical Physics 35, no. 10 (October 1996): 2057–74. http://dx.doi.org/10.1007/bf02302226.

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11

Manjavidze, J., and A. Sissakian. "Symmetries, variational principles, and quantum dynamics." Discrete Dynamics in Nature and Society 2004, no. 1 (2004): 205–12. http://dx.doi.org/10.1155/s1026022604310022.

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We describe the role of symmetries in formation of quantum dynamics. A quantum version of d'Alembert's principle is proposed to take into account the symmetry constrains more exact. It is argued that the time reversibility of quantum process, as the quantum analogy of d'Alembert's principle, makes the measure of the corresponding path integralδ-like. The argument of thisδ-function is the sum of all classical forces of the problem under consideration plus the random force of quantum excitations. Such measure establishes the one-to-one correspondence with classical mechanics and, for this reason, allows a free choice of the useful dynamical variables. The analysis shows that choosing the action-angle variables, one may get to the free-from-divergences quantum field theory. Moreover, one can try to get an independence from necessity to extract the degrees of freedom constrained by the symmetry. These properties of new quantization scheme are vitally essential for such theories as the non-Abelian Yang-Mills gauge theory and quantum gravity.

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12

Wang, Shumei, Pengao Xu, Ruicheng Song, Peiyao Li, and Hongyang Ma. "Development of High Performance Quantum Image Algorithm on Constrained Least Squares Filtering Computation." Entropy 22, no. 11 (October 25, 2020): 1207. http://dx.doi.org/10.3390/e22111207.

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Recent development of computer technology may lead to the quantum image algorithms becoming a hotspot. Quantum information and computation give some advantages to our quantum image algorithms, which deal with the limited problems that cannot be solved by the original classical image algorithm. Image processing cry out for applications of quantum image. Most works on quantum images are theoretical or sometimes even unpolished, although real-world experiments in quantum computer have begun and are multiplying. However, just as the development of computer technology helped to drive the Technology Revolution, a new quantum image algorithm on constrained least squares filtering computation was proposed from quantum mechanics, quantum information, and extremely powerful computer. A quantum image representation model is introduced to construct an image model, which is then used for image processing. Prior knowledge is employed in order to reconstruct or estimate the point spread function, and a non-degenerate estimate is obtained based on the opposite processing. The fuzzy function against noises is solved using the optimal measure of smoothness. On the constraint condition, determine the minimum criterion function and estimate the original image function. For some motion blurs and some kinds of noise pollutions, such as Gaussian noises, the proposed algorithm is able to yield better recovery results. Additionally, it should be noted that, when there is a noise attack with very low noise intensity, the model based on the constrained least squares filtering can still deliver good recovery results, with strong robustness. Subsequently, discuss the simulation analysis of the complexity of implementing quantum circuits and image filtering, and demonstrate that the algorithm has a good effect on fuzzy recovery, when the noise density is small.

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13

Oaknin, David H. "Are models of local hidden variables for the singlet polarization state necessarily constrained by the Bell inequality?" Modern Physics Letters A 35, no. 28 (June 25, 2020): 2050229. http://dx.doi.org/10.1142/s0217732320502296.

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The Bell inequality is thought to be a common constraint shared by all models of local hidden variables that aim to describe the entangled states of two qubits. Since the inequality is violated by the quantum mechanical description of these states, it purportedly allows distinguishing in an experimentally testable way the predictions of quantum mechanics from those of models of local hidden variables and, ultimately, ruling the latter out. In this paper, we show, however, that the models of local hidden variables constrained by the Bell inequality all share a subtle, though crucial, feature that is not required by fundamental physical principles and, hence, it might not be fulfilled in the actual experimental setup that tests the inequality. Indeed, the disputed feature neither can be properly implemented within the standard framework of quantum mechanics and it is even at odds with the fundamental principle of relativity. Namely, the proof of the inequality requires the existence of a preferred absolute frame of reference (supposedly provided by the lab) with respect to which the hidden properties of the entangled particles and the orientations of each one of the measurement devices that test them can be independently defined through a long sequence of realizations of the experiment. We notice, however, that while the relative orientation between the two measurement devices is a properly defined physical magnitude in every single realization of the experiment, their global rigid orientation with respect to a lab frame is a spurious gauge degree of freedom. Following this observation, we were able to explicitly build a model of local hidden variables that does not share the disputed feature and, hence, it is able to reproduce the predictions of quantum mechanics for the entangled states of two qubits.

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14

Grundling, Hendrik, and C. A. Hurst. "Constrained dynamics for quantum mechanics. I. Restricting a particle to a surface." Journal of Mathematical Physics 39, no. 6 (June 1998): 3091–119. http://dx.doi.org/10.1063/1.532241.

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15

Dunlap, Brett I., and Igor V. Schweigert. "Self-consistent, constrained linear-combination-of-atomic-potentials approach to quantum mechanics." Journal of Chemical Physics 134, no. 4 (January 28, 2011): 044122. http://dx.doi.org/10.1063/1.3524340.

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16

PERVUSHIN, V., and T. TOWMASJAN. "OBSERVABLE TIME IN QUANTUM COSMOLOGY." International Journal of Modern Physics D 04, no. 01 (February 1995): 105–13. http://dx.doi.org/10.1142/s0218271895000089.

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We show that the first principles of quantization and the experience of relativistic quantum mechanics can lead to the definition of observable time in quantum cosmology as a global quantity which coincides with the constrained action of the reduced theory up to the energy factor. The latter is fixed by the correspondence principle once one considers the limit of the “dust filled” Universe. The “global time” interpolates between the proper time for dust dominance and the conformal time for radiation dominance.

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17

Solé, A., X. Oriols, D. Marian, and N. Zanghì. "How Does Quantum Uncertainty Emerge from Deterministic Bohmian Mechanics?" Fluctuation and Noise Letters 15, no. 03 (September 2016): 1640010. http://dx.doi.org/10.1142/s0219477516400101.

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Bohmian mechanics is a theory that provides a consistent explanation of quantum phenomena in terms of point particles whose motion is guided by the wave function. In this theory, the state of a system of particles is defined by the actual positions of the particles and the wave function of the system; and the state of the system evolves deterministically. Thus, the Bohmian state can be compared with the state in classical mechanics, which is given by the positions and momenta of all the particles, and which also evolves deterministically. However, while in classical mechanics it is usually taken for granted and considered unproblematic that the state is, at least in principle, measurable, this is not the case in Bohmian mechanics. Due to the linearity of the quantum dynamical laws, one essential component of the Bohmian state, the wave function, is not directly measurable. Moreover, it turns out that the measurement of the other component of the state — the positions of the particles — must be mediated by the wave function; a fact that in turn implies that the positions of the particles, though measurable, are constrained by absolute uncertainty. This is the key to understanding how Bohmian mechanics, despite being deterministic, can account for all quantum predictions, including quantum randomness and uncertainty.

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18

French, Alfred D., and Glenn P. Johnson. "Quantum mechanics studies of cellobiose conformations." Canadian Journal of Chemistry 84, no. 4 (April 1, 2006): 603–12. http://dx.doi.org/10.1139/v06-050.

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Three regions of the conformation space that describes the relative orientations of the two glucose residues of cellobiose were analyzed with quantum mechanics. A central region, in which most crystal structures are found, was covered by a 9 × 9 grid of 20° increments of the linkage torsion angles ϕ and ψ. Besides these 81 constrained minimizations, we studied two central subregions and two regions at the edges of our maps of complete ϕ,ψ space with unconstrained minimization, for a total of 85 target geometries. HF/6-31G(d) and single-point HF/6-311+G(d) calculations were used to find the lowest energies for each geometry. B3LYP/6-31G+G(d) and single point B3LYP/6-11+G(d) calculations were also used for all unconstrained minimizations. For each target, 181 starting geometries were tried (155 for the unconstrained targets). Numerous different starting geometries resulted in the lowest energies for the various target structures. The starting geometries came from five different sets that were based on molecular mechanics energies. Although all five sets contributed to the adiabatic map, use of any single set resulted in discrepancies of 37 kcal/mol (1 cal = 4.184 J) with the final map. For most of the targets, the starting geometry that gave the lowest energy depended on the basis set and whether the HF or B3LYP method was used. However, each of the above four calculations gave the same overall lowest energy structure that was found previously by Strati et al. This global minimum, stabilized by highly cooperative hydrogen bonds, is in a region that is essentially not populated by crystal structures. HF/6-31G(d) energy contours of the mapped central region were compatible with the observed crystal structures. Observed structures that lacked O3···O5′ hydrogen bonds were about 1 kcal/mol above the map's minimum, and observed structures that have a pseudo twofold screw axis ranged from about 0.4 to 1.0 kcal/mol. The HF/6-311+G(d) map accommodated the observed structures nearly as well.Key words: cellulose, carbohydrate, conformation, energy, flexibility, folding, helix, shape.

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19

Panahi, H., and L. Jahangiri. "Quantum mechanics of a constrained particle on an ellipsoid: Bein formalism and Geometric momentum." Annals of Physics 372 (September 2016): 57–67. http://dx.doi.org/10.1016/j.aop.2016.04.013.

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20

da Silva, Luiz C. B., Cristiano C. Bastos, and Fábio G. Ribeiro. "Quantum mechanics of a constrained particle and the problem of prescribed geometry-induced potential." Annals of Physics 379 (April 2017): 13–33. http://dx.doi.org/10.1016/j.aop.2017.02.012.

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21

VARMA, RAM K. "TOPOLOGICAL MANIFESTATIONS IN CLASSICAL MECHANICS: DISCRETE ALLOWED AND FORBIDDEN STATES OF MOTION." Modern Physics Letters A 09, no. 39 (December 21, 1994): 3653–61. http://dx.doi.org/10.1142/s021773239400349x.

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Consequences of the topology of the configuration space of a Hamiltonian dynamical system are considered for a coherent system of trajectories. It is shown that when the space is multiply-connected and therefore the action integral is multivalued, the allowed states of motion (labeled by the initial data) are constrained to a discrete set by the requirement that the action be single-valued. One thus obtains a quantum-like discretization of allowed states of motion even in classical mechanics. Such discrete “allowed” and “forbidden” states have indeed been observed in the classical mechanical system of charged particles in a magnetic field. The relationship of this formalism with a Schrödinger-like formalism for the latter problem given earlier is discussed.

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22

Hsu, Stephen D. H. "The measure problem in no-collapse (many worlds) quantum mechanics." International Journal of Modern Physics D 26, no. 03 (February 3, 2017): 1730008. http://dx.doi.org/10.1142/s0218271817300087.

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We explain the measure problem (cf. origin of the Born probability rule) in no-collapse quantum mechanics. Everett defined maverick branches of the state vector as those on which the usual Born probability rule fails to hold — these branches exhibit highly improbable behaviors, including possibly the breakdown of decoherence or even the absence of an emergent semi-classical reality. Derivations of the Born rule which originate in decision theory or subjective probability (i.e. the reasoning of individual observers) do not resolve this problem, because they are circular: they assume, a priori, that the observer occupies a non-maverick branch. An ab initio probability measure is sometimes assumed to explain why we do not occupy a maverick branch. This measure is constrained by, e.g. Gleason’s theorem or envariance to be the usual Hilbert measure. However, this ab initio measure ultimately governs the allocation of a self or a consciousness to a particular branch of the wave function, and hence invokes primitives which lie beyond the Everett wave function and beyond what we usually think of as physics. The significance of this leap has been largely overlooked, but requires serious scrutiny.

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23

Baym, Gordon, and D. H. Beck. "Elementary quantum mechanics of the neutron with an electric dipole moment." Proceedings of the National Academy of Sciences 113, no. 27 (June 20, 2016): 7438–42. http://dx.doi.org/10.1073/pnas.1607599113.

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The neutron, in addition to possibly having a permanent electric dipole moment as a consequence of violation of time-reversal invariance, develops an induced electric dipole moment in the presence of an external electric field. We present here a unified nonrelativistic description of these two phenomena, in which the dipole moment operator, D→, is not constrained to lie along the spin operator. Although the expectation value of D→ in the neutron is less than 10−13 of the neutron radius, rn, the expectation value of D→ 2 is of order rn2. We determine the spin motion in external electric and magnetic fields, as used in past and future searches for a permanent dipole moment, and show that the neutron electric polarizability, although entering the neutron energy in an external electric field, does not affect the spin motion. In a simple nonrelativistic model we show that the expectation value of the permanent dipole is, to lowest order, proportional to the product of the time-reversal-violating coupling strength and the electric polarizability of the neutron.

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24

Khan, Muhammad Mubashir, Asad Arfeen, Usama Ahsan, Saneeha Ahmed, and Tahreem Mumtaz. "Analysis of achievable distances of BB84 and KMB09 QKD protocols." International Journal of Quantum Information 18, no. 06 (September 2020): 2050033. http://dx.doi.org/10.1142/s0219749920500331.

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Quantum key distribution (QKD) is a proven secured way to transmit shared secret keys using quantum particles. Any adversarial attempt to intercept and eavesdrop secret key results in generating errors alerting the legitimate users. Since QKD is constrained by quantum mechanics principles, the practical transmission of the key at a greater distance is an issue. In this paper, we discover and analyze the key factors associated with transmission media, hardware components and protocol implementation of the QKD system that causes hindrance in distance range. Practical implementation of BB84 and KMB09 protocols is discussed to determine the achievable distance given current technology. We find that by using ultra low loss fiber, short-pulse laser and superconducting nanowire single photon detector the maximum achievable distance for both of the quantum protocols is 250[Formula: see text]km.

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Bastos, Cristiano C., Antonio C. Pavão, and Eduardo S. G. Leandro. "On the quantum mechanics of a particle constrained to generalized cylinders with application to Möbius strips." Journal of Mathematical Chemistry 54, no. 9 (June 6, 2016): 1822–34. http://dx.doi.org/10.1007/s10910-016-0652-5.

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26

Yang, Jianhao M. "Switching Quantum Reference Frames for Quantum Measurement." Quantum 4 (June 18, 2020): 283. http://dx.doi.org/10.22331/q-2020-06-18-283.

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Physical observation is made relative to a reference frame. A reference frame is essentially a quantum system given the universal validity of quantum mechanics. Thus, a quantum system must be described relative to a quantum reference frame (QRF). Further requirements on QRF include using only relational observables and not assuming the existence of external reference frame. To address these requirements, two approaches are proposed in the literature. The first one is an operational approach (F. Giacomini, et al, Nat. Comm. 10:494, 2019) which focuses on the quantization of transformation between QRFs. The second approach attempts to derive the quantum transformation between QRFs from first principles (A. Vanrietvelde, et al, Quantum 4:225, 2020). Such first principle approach describes physical systems as symmetry induced constrained Hamiltonian systems. The Dirac quantization of such systems before removing redundancy is interpreted as perspective-neutral description. Then, a systematic redundancy reduction procedure is introduced to derive description from perspective of a QRF. The first principle approach recovers some of the results from the operational approach, but not yet include an important part of a quantum theory - the measurement theory. This paper is intended to bridge the gap. We show that the von Neumann quantum measurement theory can be embedded into the perspective-neutral framework. This allows us to successfully recover the results found in the operational approach, with the advantage that the transformation operator can be derived from the first principle. In addition, the formulation presented here reveals several interesting conceptual insights. For instance, the projection operation in measurement needs to be performed after redundancy reduction, and the projection operator must be transformed accordingly when switching QRFs. These results represent one step forward in understanding how quantum measurement should be formulated when the reference frame is also a quantum system.

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FANIANDARI, Suci, A. SUPARMI, and C. CARI. "ANALYTICAL SOLUTION OF SCHRÖDINGER EQUATION FOR YUKAWA POTENTIAL WITH VARIABLE MASS IN TOROIDAL COORDINATE USING SUPERSYMMETRIC QUANTUM MECHANICS." Periódico Tchê Química 17, no. 35 (July 20, 2020): 100–108. http://dx.doi.org/10.52571/ptq.v17.n35.2020.10_faniandari_pgs_100_108.pdf.

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Schrodinger equation on a toroidal coordinate was proposed in theoretical physics to get the information and the behavior of the system of particle. It was solved just recently in case of a charged scalar particle interacting with a uniform magnetic field, a uniform electric field, and a neutral charge constrained to the surface. The methodology used in the referred work was to solve the Schrodinger equation using an approach outlined in the Whittaker-Watson treatise, which deals with an infinite-dimensional eigenvalue problem and specific particular values of the applied field for eigenfunction problem. In contrast, in the quantum mechanical problem, one had an infinite-dimensional generalized eigenvalue problem. This study aimed to obtain the non-relativistic energy eigenvalue and the radial wave function of the Schrodinger equation under the influence of Yukawa potential. The Supersymmetric Quantum Mechanics (SUSY QM) method was used as a basis to tackle the primary objective of this paper to study the problem of a particle with variable mass in toroidal coordinate. The proper super potential was used to deal with the hyperbolic form of effective potential, and the energy spectra were calculated for different quantum numbers, potential depth, and potential parameters. The radial wave function equation for ground and excited state were obtained. The results showed that the increasing value of the quantum numbers caused the energy spectra of the system to increase to the highest value when the quantum number was equal to the potential parameter, which means the most effective energy value was produced, then it was decreased afterward. While the energy value did not depend on the change of the potential parameter. This property could be used to produce this equation as an application of the previous results, the Schrödinger eigenfunction was used as the starting points to solve the other equation in the same geometrical setting and potential.

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Carson, Cathryn. "Who Wants a Postmodern Physics?" Science in Context 8, no. 4 (1995): 635–55. http://dx.doi.org/10.1017/s0269889700002222.

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The ArgumentTheorists of science and culture, seeking to explicate the implications of chaos theory, quantum mechanics, or special and general relativity, have drawn parallels to the constellation of intellectual and social phenomena collected in the concept of postmodernism. The notion thereby invoked of a postmodern physics is suggestive and worth exploring. But it remains ungrounded so long as the argument moves in the realm of parallels. Moreover, these discussions prove to be tacitly constrained by a preexisting genre of physicists' own literary production, a genre whose argumentative structures have been taken over implicitly into the subsequent exchanges. Attending critically in this way to the intellectual interests of the discussants — asking who it is that wants to constitute a postmodern physics — should open up more productive ways of framing the debate.

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XUN, D. M., and Q. H. LIU. "GEOMETRIC MOMENTUM IN THE MONGE PARAMETRIZATION OF TWO-DIMENSIONAL SPHERE." International Journal of Geometric Methods in Modern Physics 10, no. 03 (January 10, 2013): 1220031. http://dx.doi.org/10.1142/s0219887812200319.

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A two-dimensional (2D) surface can be considered as three-dimensional (3D) shell whose thickness is negligible in comparison with the dimension of the whole system. The quantum mechanics on surface can be first formulated in the bulk and the limit of vanishing thickness is then taken. The gradient operator and the Laplace operator originally defined in bulk converges to the geometric ones on the surface, and the so-called geometric momentum and geometric potential are obtained. On the surface of 2D sphere the geometric momentum in the Monge parametrization is explicitly explored. Dirac's theory on second-class constrained motion is resorted to for accounting for the commutator [xi, pj] = iℏ(δij - xixj/r2) rather than [xi, pj] = iℏδij that does not hold true anymore. This geometric momentum is geometric invariant under parameters transformation, and self-adjoint.

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KHEYFETS, ARKADY, DANIEL E. HOLZ, and WARNER A. MILLER. "THE ISSUE OF TIME EVOLUTION IN QUANTUM GRAVITY." International Journal of Modern Physics A 11, no. 16 (June 30, 1996): 2977–3002. http://dx.doi.org/10.1142/s0217751x96001450.

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We discuss the relation between the concept of time and the dynamic structure of quantum gravity. We briefly review the problems of time associated with the standard procedures of gravity quantization. By explicitly utilizing York’s analysis of the geometrodynamic degrees of freedom, and imposing the constraints as expectation value equations, we describe a new procedure of gravity quantization. In particular, this “minimally constrained canonical” quantization procedure leads to a linear Schrödinger equation augmented by the super-Hamiltonian and supermomentum constraints imposed on expectation values. This approach supplies a description of time evolution in quantum geometrodynamics free from the standard problems of time associated with canonical approaches. Furthermore, the theory is applicable to the full theory of general relativity, without the need to impose symmetries or reduce dimensionality. Using this method we arrive at an analytic expression for the quantum evolution of the Kasner cosmology, as well as a numerically generated solution of the quantized Taub model. The key new feature of this approach is that we impose the constraints weakly — instead of the quantum-mechanical wave function satisfying the constraints exactly, it need only satisfy them on average. Thus the constraints only constrain the observables.

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31

Nalewajski, Roman F. "Understanding Electronic Structure and Chemical Reactivity: Quantum-Information Perspective." Applied Sciences 9, no. 6 (March 26, 2019): 1262. http://dx.doi.org/10.3390/app9061262.

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Several applications of quantum mechanics and information theory to chemical reactivity problems are presented with emphasis on equivalence of variational principles for the constrained minima of the system electronic energy and its kinetic energy component, which also determines the overall gradient information. Continuities of molecular probability and current distributions, reflecting the modulus and phase components of molecular wavefunctions, respectively, are summarized. Resultant measures of the entropy/information descriptors of electronic states, combining the classical (probability) and nonclassical (phase/current) contributions, are introduced, and information production in quantum states is shown to be of a nonclassical origin. Importance of resultant information descriptors for distinguishing the bonded (entangled) and nonbonded (disentangled) states of reactants in acid(A)–base(B) systems is stressed and generalized entropy concepts are used to determine the phase equilibria in molecular systems. The grand-canonical principles for the minima of electronic energy and overall gradient information allow one to explore relations between energetic and information criteria of chemical reactivity in open molecules. The populational derivatives of electronic energy and resultant gradient information give identical predictions of electronic flows between reactants. The role of electronic kinetic energy (resultant gradient information) in chemical-bond formation is examined, the virial theorem implications for the Hammond postulate of reactivity theory are explored, and changes of the overall structure information in chemical processes are addressed. The frontier-electron basis of the hard (soft) acids and bases (HSAB) principle is reexamined and covalent/ionic characters of the intra- and inter-reactant communications in donor-acceptor systems are explored. The complementary A–B coordination is compared with its regional HSAB analog, and polarizational/relaxational flows in such reactive systems are explored.

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32

Yang, Weitao, Chenyang Xiang, Yan Xu, Shizhen Chen, Weiwei Zeng, Kai Liu, Xiao Jin, Xin Zhou, and Bingbo Zhang. "Albumin-constrained large-scale synthesis of renal clearable ferrous sulfide quantum dots for T1-Weighted MR imaging and phototheranostics of tumors." Biomaterials 255 (October 2020): 120186. http://dx.doi.org/10.1016/j.biomaterials.2020.120186.

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33

Mannhart, Jochen. "Beyond Superconductivity." Journal of Superconductivity and Novel Magnetism 33, no. 1 (September 12, 2019): 249–51. http://dx.doi.org/10.1007/s10948-019-05286-3.

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Abstract We present a novel device concept that utilizes the fascinating transition regime between quantum mechanics and classical physics. The devices operate by using a small number of individual quantum mechanical collapse events to interrupt the unitary evolution of quantum states represented by wave packets. Exceeding the constraints of the unitary evolution of quantum mechanics given by Schrödinger’s equation and of classical Hamiltonian physics, these devices display a surprising behavior.

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34

Costa, R. C. T. da. "Constraints in quantum mechanics." European Journal of Physics 7, no. 4 (October 1, 1986): 269–73. http://dx.doi.org/10.1088/0143-0807/7/4/010.

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Lasukova, Tatiana, Vladimir Lasukov, and Maria Abdrashitova. "Quantum mechanics with geometric constraints of Friedmann type." Open Physics 15, no. 1 (August 10, 2017): 551–56. http://dx.doi.org/10.1515/phys-2017-0063.

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AbstractThe paper presents the study of quantum mechanics of a free particle with the constraints in the phase space, the canonical equations, which are the geometrical constraints of Friedmann type. It has been proved that the constraints can imitate force. As well as in quantum geometrodynamics with Logunov constraints, in quantum mechanics with constraints time does not vanish

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36

Licata, Ignazio, and Leonardo Chiatti. "Event-Based Quantum Mechanics: A Context for the Emergence of Classical Information." Symmetry 11, no. 2 (February 3, 2019): 181. http://dx.doi.org/10.3390/sym11020181.

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This paper explores an event-based version of quantum mechanics which differs from the commonly accepted one, even though the usual elements of quantum formalism, e.g., the Hilbert space, are maintained. This version introduces as primary element the occurrence of micro-events induced by usual physical (mechanical, electromagnetic and so on) interactions. These micro-events correspond to state reductions and are identified with quantum jumps, already introduced by Bohr in his atomic model and experimentally well established today. Macroscopic bodies are defined as clusters of jumps; the emergence of classicality thus becomes understandable and time honoured paradoxes can be solved. In particular, we discuss the cat paradox in this context. Quantum jumps are described as temporal localizations of physical quantities; if the information associated with these localizations has to be finite, two time scales spontaneously appear: an upper cosmological scale and a lower scale of elementary “particles”. This allows the interpretation of the Bekenstein limit like a particular informational constraint on the manifestation of a micro-event in the cosmos it belongs. The topic appears relevant in relation to recent discussions on possible spatiotemporal constraints on quantum computing.

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37

Kumar, Ashok, B. L. Jhanwar, and William J. Meath. "Dipole Oscillator Strength Distributions and Properties for Methanol, Ethanol and Propan-1-ol and Related Dispersion Energies." Collection of Czechoslovak Chemical Communications 70, no. 8 (2005): 1196–224. http://dx.doi.org/10.1135/cccc20051196.

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Recommended isotropic dipole oscillator strength distributions (DOSDs) have been constructed for the methanol and ethanol molecules through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength (DOS) data; the DOS data employed are recent experimental results not available at the time of the original constrained DOSD analysis of these molecules. The constraints are furnished by molar refractivity data and the Thomas-Reiche-Kuhn sum rule. The DOSDs are used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for the molecules. Pseudo-DOSDs for these molecules, and for propan-1-ol based on an earlier constrained DOSD analysis for this molecule, are also presented. They are used to obtain reliable results for the isotropic dipole-dipole dispersion energy coefficients C6, for the interactions of the alcohols with each other and with 36 other species, and the triple-dipole dispersion energy coefficients C9for interactions involving any triple of molecules involving methanol, ethanol and propan-1-ol.

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38

Sokolovski, Dmitri, and Alexandre Matzkin. "Wigner’s Friend Scenarios and the Internal Consistency of Standard Quantum Mechanics." Entropy 23, no. 9 (September 9, 2021): 1186. http://dx.doi.org/10.3390/e23091186.

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Wigner’s friend scenarios involve an Observer, or Observers, measuring a Friend, or Friends, who themselves make quantum measurements. In recent discussions, it has been suggested that quantum mechanics may not always be able to provide a consistent account of a situation involving two Observers and two Friends. We investigate this problem by invoking the basic rules of quantum mechanics as outlined by Feynman in the well-known “Feynman Lectures on Physics”. We show here that these “Feynman rules” constrain the a priori assumptions which can be made in generalised Wigner’s friend scenarios, because the existence of the probabilities of interest ultimately depends on the availability of physical evidence (material records) of the system’s past. With these constraints obeyed, a non-ambiguous and consistent account of all measurement outcomes is obtained for all agents, taking part in various Wigner’s Friend scenarios.

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39

ELLIS, JOHN, N. E. MAVROMATOS, and D. V. NANOPOULOS. "CPT VIOLATION IN STRING-MODIFIED QUANTUM MECHANICS AND THE NEUTRAL-KAON SYSTEM." International Journal of Modern Physics A 11, no. 08 (March 30, 1996): 1489–507. http://dx.doi.org/10.1142/s0217751x96000687.

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We argue that CPT is in general violated in a non-quantum-mechanical way in the effective low-energy theory derived from noncritical string theory, in which pure states evolve into mixed states in general. It is known that such a dynamical framework violates the strong form of CPT invariance. We relate CPT violation in the effective low-energy theory in our formalism to apparent world-sheet charge nonconservation induced by stringy monopoles corresponding to target-space black-hole configurations. We prove that energy is conserved on the average in this CPT-violating modification of quantum mechanics. The magnitude of the effective spontaneous violation of CPT may not be far from the present experimental sensitivity in the neutral-kaon system. We demonstrate that previously proposed phenomenological modifications to the quantum-mechanical description of the neutral-kaon system violate CPT, although in a different way from that assumed in analyses within conventional quantum mechanics. We sketch the way to constrain the novel CPT-violating parameters using available data on KL→2π, KS→ 3π0 and semileptonic KL,S decay asymmetries. Could non-quantum-field-theoretical and non-quantum-mechanical CPT violation usher in the long-awaited era of string phenomenology?

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40

Kumar, A., B. L. Jhanwar, and W. Meath. "Dipole oscillator strength distributions, properties, and dispersion energies for ethylene, propene, and 1-butene." Canadian Journal of Chemistry 85, no. 10 (October 1, 2007): 724–37. http://dx.doi.org/10.1139/v07-057.

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A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the ethylene molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength (DOS) data; the DOS data employed are recent experimental results not available at the time of the original constrained DOSD analysis of this molecule. The constraints are furnished by molar refractivity data and the Thomas–Reiche–Kuhn sum rule. The DOSD is used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for ethylene. Pseudo-DOSDs for this molecule, and for propene and 1–butene, which are based on an earlier constrained DOSD analysis for these molecules, are developed. They are used to obtain reliable results for the isotropic dipole–dipole dispersion-energy coefficients C6, for the interactions of the alkenes with each other and with 47 other species, and the triple-dipole dispersion-energy coefficients C9 for interactions involving any triple of molecules taken from ethylene, propene, and 1–butene.Key words: alkenes, dipole properties, pseudo-states, dipole–dipole and triple-dipole dispersion energies, long-range additive, non-additive interaction energies.

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41

HAN, MUXIN, YONGGE MA, and WEIMING HUANG. "FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY." International Journal of Modern Physics D 16, no. 09 (September 2007): 1397–474. http://dx.doi.org/10.1142/s0218271807010894.

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In the recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, non-perturbative quantum theory for a Lorentzian gravitational field on a four-dimensional manifold. In the approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of, so-called, quantum Riemannian geometry, which is discrete on the fundamental scale. Imposing the quantum constraints in analogy from the classical ones, the quantum dynamics of gravity is being studied as one of the most important issues in loop quantum gravity. On the other hand, the semi-classical analysis is being carried out to test the classical limit of the quantum theory. In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of the kinematical Ashtekar–Isham–Lewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to obtain other background-independent quantum gauge theories. There is no divergence within this background-independent and diffeomorphism-invariant quantization program of matter coupled to gravity.

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Gorobey, Natalia, and Alexander Lukyanenko. "Ground state of the universe in quantum cosmology." International Journal of Modern Physics A 31, no. 02n03 (January 20, 2016): 1641014. http://dx.doi.org/10.1142/s0217751x16410141.

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We find a physical state of a closed universe with the minimal excitation of the universe expansion energy in quantum gravity. It is an analog of the vacuum state of the ordinary quantum field theory in the Minkowsky space, but in our approach an energy of space of a closed universe together with the energy of its matter content are minimized. This ground state is chosen among an enlarged set of physical states, compared with the ordinary covariant quantum gravity. In our approach, physical states are determined by weak constraints: quantum mechanical averages of gravitational constraint operators equal zero. As a result, they appear to be non-static in such a modification of quantum gravity. Quantum dynamics of the universe is described by Schrödinger equation with a cosmic time determined by weak gravitational constraints. In order to obtain the observed megascopic universe with the inflation stage just after its quantum beginning, a lot of the energy in the form of the inflaton scalar field condensate is prescribed to the initial state. Parameters of the initial state for a homogeneous model of the universe are calculated.

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Paban, Sonia, Savdeep Sethi, and Mark Stern. "Constraints from extended supersymmetry in quantum mechanics." Nuclear Physics B 534, no. 1-2 (November 1998): 137–54. http://dx.doi.org/10.1016/s0550-3213(98)00518-5.

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44

KAUSHAL, R. S. "POSSIBILITY OF A GEOMETRIC CONSTRAINT IN THE SCHRÖDINGER QUANTUM MECHANICS." Modern Physics Letters A 15, no. 21 (July 10, 2000): 1391–97. http://dx.doi.org/10.1142/s0217732300001869.

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Within the framework of some straightforward mathematical terms it is argued that there exists a space-invariant in the Schrödinger quantum mechanics (SQM). As an alternative to the geometric features of localized nature dictated by the prescribed boundary conditions in a potential problem in SQM, this spatial invariant is expected to account for some global geometric features of the quantum system.

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45

OHNUKI, Y., and S. KITAKADO. "QUANTUM MECHANICS ON A CLOSED LOOP." Modern Physics Letters A 09, no. 02 (January 20, 1994): 143–50. http://dx.doi.org/10.1142/s0217732394000150.

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Quantum mechanics on the loop of arbitrary shape is formulated, which is an extension of previous formulations of quantum mechanics on S1 preserving its topology. It is shown that the representation spaces of the algebra do not change under the extension. We also derive, in the x-diagonal representation, the explicit expressions for the operators px and py that satisfy the constraints of the Dirac quantization on the closed loop.

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46

Delaney, P., and J. C. Greer. "Classical computation with quantum systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2065 (November 4, 2005): 117–35. http://dx.doi.org/10.1098/rspa.2005.1565.

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As semiconductor electronic devices scale to the nanometer range and quantum structures (molecules, fullerenes, quantum dots, nanotubes) are investigated for use in information processing and storage, it becomes useful to explore the limits imposed by quantum mechanics on classical computing. To formulate the problem of a quantum mechanical description of classical computing, electronic device and logic gates are described as quantum sub-systems with inputs treated as boundary conditions, outputs expressed as operator expectation values, and transfer characteristics and logic operations expressed through the sub-system Hamiltonian, with constraints appropriate to the boundary conditions. This approach, naturally, leads to a description of the sub-systems in terms of density matrices. Application of the maximum entropy principle subject to the boundary conditions (inputs) allows for the determination of the density matrix (logic operation), and for calculation of expectation values of operators over a finite region (outputs). The method allows for an analysis of the static properties of quantum sub-systems.

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47

STROBL, THOMAS. "QUANTIZATION AND THE ISSUE OF TIME FOR VARIOUS TWO-DIMENSIONAL MODELS OF GRAVITY." International Journal of Modern Physics D 03, no. 01 (March 1994): 281–84. http://dx.doi.org/10.1142/s0218271894000460.

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It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and R2-Gravity are embedded in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above systems are then presented: The Dirac constraints can be solved exactly in the momentum representation, the path integral can be integrated out, and the constraint algebra can be explicitely canonically abelianized, thus allowing also for a (superficial) reduced phase space quantization. Non-trivial dynamics are obtained by means of time dependent gauges. All of these approaches lead to the same finite dimensional quantum mechanical system.

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48

Vacchini, Bassano. "Quantum Noise from Reduced Dynamics." Fluctuation and Noise Letters 15, no. 03 (September 2016): 1640003. http://dx.doi.org/10.1142/s0219477516400034.

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We consider the description of quantum noise within the framework of the standard Copenhagen interpretation of quantum mechanics applied to a composite system environment setting. Averaging over the environmental degrees of freedom leads to a stochastic quantum dynamics, described by equations complying with the constraints arising from the statistical structure of quantum mechanics. Simple examples are considered in the framework of open system dynamics described within a master equation approach, pointing in particular to the appearance of the phenomenon of decoherence and to the relevance of quantum correlation functions of the environment in the determination of the action of quantum noise.

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Froese, Richard, and Ira Herbst. "Realizing Holonomic Constraints in Classical and Quantum Mechanics." Communications in Mathematical Physics 220, no. 3 (July 1, 2001): 489–535. http://dx.doi.org/10.1007/s002200100454.

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50

HAMADA, KEN-JI, and ASATO TSUCHIYA. "QUANTUM GRAVITY AND BLACK HOLE DYNAMICS IN 1+1 DIMENSIONS." International Journal of Modern Physics A 08, no. 27 (October 30, 1993): 4897–913. http://dx.doi.org/10.1142/s0217751x93001922.

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We study the quantum theory of 1+1 dimensional dilaton gravity, which is an interesting toy model of the black hole dynamics. The functional measures are explicitly evaluated and the physical state conditions corresponding to the Hamiltonian and the momentum constraints are derived. It is pointed out that the constraints form the Virasoro algebra without central charge. In the ADM formalism the measures are very ambiguous, but in our formalism they are explicitly defined. Then the new features which are not seen in the ADM formalism come out. A singularity appears at φ2=κ(>0), where κ=(N–51/2)/12 and N is the number of matter fields. Behind the singularity the quantum mechanical region κ>φ2>0 extends, where the sign of the kinetic term in the Hamiltonian constraint changes. If κ<0, the singularity disappears. We discuss the quantum dynamics of a black hole and then give a suggestion for the resolution of the information loss paradox. We also argue the quantization of the spherically symmetric gravitational system in 3+1 dimensions. In the appendix, the differences between the other quantum dilaton gravities and ours are clarified and our status is stressed.

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