Relevant bibliographies by topics / Quantum trajectory equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Quantum trajectory equation'

Author: Grafiati
Published: 19 February 2023
Last updated: 20 February 2023

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Journal articles on the topic "Quantum trajectory equation"

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Holland, Peter. "Trajectory construction of Dirac evolution." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2236 (2020): 20190682. http://dx.doi.org/10.1098/rspa.2019.0682.

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We extend our programme of representing the quantum state through exact stand-alone trajectory models to the Dirac equation. We show that the free Dirac equation in the angular coordinate representation is a continuity equation for which the real and imaginary parts of the wave function, angular versions of Majorana spinors, define conserved densities. We hence deduce an exact formula for the propagation of the Dirac spinor derived from the self-contained first-order dynamics of two sets of trajectories in 3-space together with a mass-dependent evolution operator. The Lorentz covariance of the
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Rahmani, Faramarz, and Mehdi Golshani. "Some clarifications about the Bohmian geodesic deviation equation and Raychaudhuri’s equation." International Journal of Modern Physics A 33, no. 03 (2018): 1850027. http://dx.doi.org/10.1142/s0217751x18500276.

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One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the definition of trajectory is possible. We do this in a fixed background and we do not consider the backre
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Avanzini, Francesco, and Giorgio J. Moro. "Quantum stochastic trajectories: the Smoluchowski–Bohm equation." Physical Chemistry Chemical Physics 20, no. 1 (2018): 165–79. http://dx.doi.org/10.1039/c7cp06071h.

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Goan, H.-S. "An analysis of reading out the state of a charge quantum bit." Quantum Information and Computation 3, no. 2 (2003): 121–38. http://dx.doi.org/10.26421/qic3.2-4.

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We provide a unified picture for the master equation approach and the quantum trajectory approach to a measurement problem of a two-state quantum system (a qubit), an electron coherently tunneling between two coupled quantum dots (CQD's) measured by a low transparency point contact (PC) detector. We show that the master equation of ``partially'' reduced density matrix can be derived from the quantum trajectory equation (stochastic master equation) by simply taking a ``partial'' average over the all possible outcomes of the measurement. If a full ensemble average is taken, the traditional (unco
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Carmichael, H. J., and Kisik Kim. "A quantum trajectory unraveling of the superradiance master equation." Optics Communications 179, no. 1-6 (2000): 417–27. http://dx.doi.org/10.1016/s0030-4018(99)00694-x.

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Doherty, Andrew C., A. Szorkovszky, G. I. Harris, and W. P. Bowen. "The quantum trajectory approach to quantum feedback control of an oscillator revisited." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1979 (2012): 5338–53. http://dx.doi.org/10.1098/rsta.2011.0531.

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We revisit the stochastic master equation approach to feedback cooling of a quantum mechanical oscillator undergoing position measurement. By introducing a rotating wave approximation for the measurement and bath coupling, we can provide a more intuitive analysis of the achievable cooling in various regimes of measurement sensitivity and temperature. We also discuss explicitly the effect of backaction noise on the characteristics of the optimal feedback. The resulting rotating wave master equation has found application in our recent work on squeezing the oscillator motion using parametric driv
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Jeong, Yeuncheol. "A COMPLETE RE-DERIVATION OF THE HIDDEN VARIABLE EQUATION IN DAVID BOHM’S 1952 PAPERS." International Journal of Applied Science and Engineering Review 03, no. 03 (2022): 18–23. http://dx.doi.org/10.52267/ijaser.2022.3304.

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Schrodinger’s equation is a basic mathematical expression for a single particle in quantum mechanics. However, its physical meaning has never been assigned in any standard quantum mechanics text book. Here, a detailed complete re-derivation of hidden variable equation in David Bohm’s 1952 papers is given to assign some physical meanings to Schrodinger’s equation. This work shows some required detailed transformation of Schrodinger’s Equation into a form of Newtonian second law of motion with definite trajectory with some initial conditions given. All the quantum effects come from the single lo
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Garashchuk, Sophya, Vaibhav Dixit, Bing Gu, and James Mazzuca. "The Schrödinger equation with friction from the quantum trajectory perspective." Journal of Chemical Physics 138, no. 5 (2013): 054107. http://dx.doi.org/10.1063/1.4788832.

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Donoso, Arnaldo, and Craig C. Martens. "Classical trajectory-based approaches to solving the quantum Liouville equation." International Journal of Quantum Chemistry 90, no. 4-5 (2002): 1348–60. http://dx.doi.org/10.1002/qua.10377.

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Vacchini, Bassano. "General structure of quantum collisional models." International Journal of Quantum Information 12, no. 02 (2014): 1461011. http://dx.doi.org/10.1142/s0219749914610115.

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We point to the connection between a recently introduced class of non-Markovian master equations and the general structure of quantum collisional models. The basic construction relies on three basic ingredients: a collection of time dependent completely positive maps, a completely positive trace preserving transformation and a waiting time distribution characterizing a renewal process. The relationship between this construction and a Lindblad dynamics is clarified by expressing the solution of a Lindblad master equation in terms of demixtures over different stochastic trajectories for the stat
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Dissertations / Theses on the topic "Quantum trajectory equation"

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Oxtoby, Neil Paul. "Keeping it real': A Quantum Trajectory Approach to Realistic Measurement of Solid-State Quantum Systems." Thesis, Griffith University, 2007. http://hdl.handle.net/10072/365770.

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To obtain information about a system of interest a measurement has to be made. In experiments that probe the quantum nature of our world, the system itself is, in general, necessarily affected by the act of measurement. If the system is weakly coupled to its bath and the dynamics are such that information concerning the system is spread throughout the many degrees of freedom of the bath, and the bath is being measured then a stochastic master equation for the conditioned state of the system can be found. This is termed a quantum trajectory equation. Realistic detectors are not perfect. Inform
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Cayayan, Lyndon Mark D. "Collective Quantum Jumps of Rydberg Atoms Undergoing Two-Channel Spontaneous Emission." Miami University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=miami1470410030.

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Vadapalli, Ravi K. "Accuracy study of a free particle using quantum trajectory method on message passing architecture." Master's thesis, Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-11062002-142043.

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Yang-HsuanLin and 林揚軒. "Reconstructing Quantum Trajectory by Solving Stochastic Differential Equation." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/58u9ph.

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碩士<br>國立成功大學<br>航空太空工程學系<br>104<br>Trajectory interpretation and probability interpretation are two opposite interpretations of quantum mechanics. The complex mechanics unifies the two interpretations by showing that the distribution of the collected trajectory points follows the statistic pattern predicted by the probability interpretation. However, there still exist slight discrepancies between the two interpretations. The first discrepancy comes from the numerical errors in the computation of trajectory points, while the second comes from the statistical error caused by the inadequacy of th
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Chou, Chia-Chun. "Analytical study of complex quantum trajectories." Thesis, 2009. http://hdl.handle.net/2152/ETD-UT-2009-05-36.

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Quantum trajectories are investigated within the complex quantum Hamilton-Jacobi formalism. A unified description is presented for complex quantum trajectories for one-dimensional time-dependent and time-independent problems. Complex quantum trajectories are examined for the free Gaussian wave packet, the coherent state in the harmonic potential, and the the barrier scattering problems. We analyze the variations of the complex-valued kinetic energy, the classical potential, and the quantum potential along the complex quantum trajectories. For one-dimensional time-independent scattering problem
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Trahan, Corey Jason. "Trajectory integration of the quantum hydrodynamic equations of motion." Thesis, 2003. http://hdl.handle.net/2152/1010.

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Trahan, Corey Jason Wyatt Robert E. "Trajectory integration of the quantum hydrodynamic equations of motion." 2003. http://wwwlib.umi.com/cr/utexas/fullcit?p3120306.

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Book chapters on the topic "Quantum trajectory equation"

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Nitzan, Abraham. "Introduction To Quantum Relaxation Processes." In Chemical Dynamics in Condensed Phases. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198529798.003.0015.

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The first question to ask about the phenomenon of relaxation is why it occurs at all. Both the Newton and the Schrödinger equations are symmetrical under time reversal: The Newton equation, dx/dt = v ; dv/dt = −∂V/∂x, implies that particles obeying this law of motion will retrace their trajectory back in time after changing the sign of both the time t and the particle velocities v. The Schrödinger equation, ∂ψ/∂t = −(i/.h) Ĥ ψ, implies that if (ψ (t) is a solution then ψ *(−t) is also one, so that observables which depend on |ψ|2 are symmetric in time. On the other hand, nature clearly evolves asymmetrically as asserted by the second law of thermodynamics. How does this asymmetry arise in a system that obeys temporal symmetry in its time evolution? Readers with background in thermodynamics and statistical mechanics have encountered the intuitive answer: Irreversibility in a system with many degrees of freedom is essentially a manifestation of the system “getting lost in phase space”:Asystem starts from a given state and evolves in time. If the number of accessible states is huge, the probability that the system will find its way back to the initial state in finite time is vanishingly small, so that an observer who monitors properties associated with the initial state will see an irreversible evolution. The question is how is this irreversible behavior manifested through the reversible equations of motion, and how does it show in the quantitative description of the time evolution. This chapter provides an introduction to this subject using the time-dependent Schrödinger equation as a starting point. Chapter 10 discusses more advanced aspects of this problem within the framework of the quantum Liouville equation and the density operator formalism.
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Nitzan, Abraham. "The Quantum Mechanical Density Operator And Its Time Evolution: Quantum Dynamics Using The Quantum Liouville Equation." In Chemical Dynamics in Condensed Phases. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198529798.003.0016.

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The starting point of the classical description of motion is the Newton equations that yield a phase space trajectory (rN (t), pN (t)) for a given initial condition (rN (0), pN (0)). Alternatively one may describe classical motion in the framework of the Liouville equation (Section (1.2.2)) that describes the time evolution of the phase space probability density f (rN , pN ; t). For a closed system fully described in terms of a well specified initial condition, the two descriptions are completely equivalent. Probabilistic treatment becomes essential in reduced descriptions that focus on parts of an overall system, as was demonstrated in Sections 5.1–5.3 for equilibrium systems, and in Chapters 7 and 8 that focus on the time evolution of classical systems that interact with their thermal environments. This chapter deals with the analogous quantum mechanical problem. Within the limitations imposed by its nature as expressed, for example, by Heisenbergtype uncertainty principles, the Schrödinger equation is deterministic. Obviously it describes a deterministic evolution of the quantum mechanical wavefunction. The analog of the phase space probability density f (rN , pN ; t) is now the quantum mechanical density operator (often referred to as the “density matrix”), whose time evolution is determined by the quantum Liouville equation. Again, when the system is fully described in terms of a well specified initial wavefunction, the two descriptions are equivalent. The density operator formalism can, however, be carried over to situations where the initial state of the system is not well characterized and/or a reduced description of part of the overall system is desired. Such situations are considered later in this chapter.
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Strasberg, Philipp. "Quantum Fluctuation Theorems." In Quantum Stochastic Thermodynamics. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780192895585.003.0004.

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Abstract We introduce a theoretical technique known as the two-point measurement scheme, which allows us to derive a variety of quantum fluctuation theorems with the same form as in classical stochastic thermodynamics. Alternatively, we show how to study fluctuations based on a quantum master equation approach combined with counting field or quantum jump trajectory methods. Although quantum fluctuation theorems have the same form as classical fluctuation theorems, they are more limited in their scope and practical applicability. Nevertheless, we study one important theoretical consequence of them, known as the thermodynamic uncertainty relation. This relation is used to discuss the impossibility of Carnot efficiency at finite power. The latter point also naturally connects to the third law of thermodynamics.
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"Conclusion." In The Quantum Classical Theory, edited by Gert D. Billing. Oxford University Press, 2003. http://dx.doi.org/10.1093/oso/9780195146196.003.0010.

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In this book, we have discussed the problems concerning mixing of classical and quantum mechanics, and we have given several possible solutions to the problem and a number of suggestions for the setup of working computational schemes. In the present chapter, we give some recommendations as to which methods one should use for a given type of system and problem. As can be seen from the tables and what is apparent from the discussion in the previous chapters, the quantum-classical method has been and is used for solving many different molecular dynamics problems. Recommendations, as far as molecule surface or processes in solution are concerned, have not been incorporated, the reason being that the methods here are still to some extent under development. We have seen that the quantum-classical approach can be derived in two different fashions. In one method the classical limit ħ→ 0 is taken in some degrees of freedom. In the other approach the quantum mechanical equations are parameterized in such a fashion that classical equations of motions are either pulled out of or injected into the quantum mechanical. Thus the first method involves and introduces the classical picture in certain particular degrees of freedom—in the second method the classical picture is in principle not introduced—it is just a reformulation of quantum mechanics. This reformulation has the exact dynamics as the limit. However, if exact calculations are to be performed, the reformulation may not be advantageous from a computational point of view, and, hence, standard methods are often more conveniently applied. We prefer the second approach for introducing the quantum-classical scheme because, as mentioned, it automatically has the exact formulation as the limit. The approach is most conveniently implemented through the trajectory driven DVR, or the so-called TDGH-DVR method, which gives the systematic way of approaching the quantum mechanical limit from the classical one. Thus, the method interpolates continuously between the classical and the quantum limit—a property it shares with, for instance, the FMS method and the Bohm formulation.
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"Second quantization." In The Quantum Classical Theory, edited by Gert D. Billing. Oxford University Press, 2003. http://dx.doi.org/10.1093/oso/9780195146196.003.0008.

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Second quantization (SQ) concepts were introduced in chapter 2 as a general tool to treat excitations in molecular collisions for which the dynamics were described in cartesian coordinates. This SQ-formulation, which was derived from the TDGH representation of the wave function, could be introduced if the potential was expanded locally to second order around the position defined by a trajectory. It is, however, possible to use the SQ approach in a number of other dynamical situations, as for instance when dealing with the vibrational excitation of diatomic and polyatomic molecules, or with energy transfer to solids and chemical reactions in the socalled reaction path formulation. Since the formal expressions in the operators are the same, irrespective of the system or dynamical situation, the algebraic manipulations are also identical, and, hence, the formal solution the same. But the dynamical input to the scheme is of course different from case to case. In the second quantization formulation of the dynamical problems, one solves the operator algebraic equations formally. Once the formal solution is obtained, we can compute the dynamical quantities which enter the expressions. The advantage over state or grid expansion methods is significant since (at least for bosons) the number of dynamical operators is much less than the number of states. In order to solve the problem to infinite order, that is, also the TDSE for the system, the operators have to form a closed set with respect to commutations. This makes it necessary to drop some two-quantum operators. Historically, the M = 1 quantum problem, namely that of a linearly forced harmonic oscillator, was solved using the operator algebraic approach by Pechukas and Light in 1966 [131]. In 1972, Kelley [128] solved the two-oscillator (M = 2) problem and the author solved the M = 3 and the general problem in 1978 [129] and 1980 [147], respectively. The general case was solved using graph theory designed for the problem and it will not be repeated here. But the formulas are given in this chapter and in the appendices B and C.
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Conference papers on the topic "Quantum trajectory equation"

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Carmichael, Howard J. "Quantum trajectory theory for cascaded open systems." In OSA Annual Meeting. Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.pd27.

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The theory of open systems is used in quantum optics in two distinct ways: to model sources of light such as lasers and parametric oscillators, and to describe the response of irradiated cavities and atoms. Sometimes the two applications are used in combination; first, statistical properties of the field radiated by a source are calculated, and these are then used in a separate calculation to determine the response of a system that is irradiated by the source. But the usefulness of this approach is quite hunted. It is essentially limited to coherent sources and certain broadband sources such a
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Carmichael, H. J., L. Tian, and P. Kochan. "Decay of quantum coherence using quantum trajectories." In OSA Annual Meeting. Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.mff4.

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In the quantum trajectory approach an open quantum system is represented by a stochastic pure-state wave function. The mixed-state density operator that satisfies the usual master equation is recovered from the quantum trajectories by performing either an ensemble average or, for stationary systems, an average over time. This unraveling of the master equation dynamics into pure-state trajectories provides new insight into the decay of quantum coherence in systems that are open to the environment. Under some conditions macroscopic superposition states are preserved as macroscopic superposition
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Wang, Yan. "Simulating Stochastic Diffusions by Quantum Walks." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12739.

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Stochastic differential equation (SDE) and Fokker-Planck equation (FPE) are two general approaches to describe the stochastic drift-diffusion processes. Solving SDEs relies on the Monte Carlo samplings of individual system trajectory, whereas FPEs describe the time evolution of overall distributions via path integral alike methods. The large state space and required small step size are the major challenges of computational efficiency in solving FPE numerically. In this paper, a generic continuous-time quantum walk formulation is developed to simulate stochastic diffusion processes. Stochastic
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von Spakovsky, Michael R., Charles E. Smith, and Vittorio Verda. "Quantum Thermodynamics for the Modeling of Hydrogen Storage on a Carbon Nanotube." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67424.

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A typical approach for modeling systems at a nanoscale in states of non-equilibrium undergoing an irreversible process is to use an ad hoc mixture of molecular dynamics (linear and nonlinear), i.e. classical mechanics, coupled to assumptions of stable equilibrium which allow one via analogy to incorporate equilibrium thermodynamic state information such as temperature and pressure into the modeling process. However, such an approach cannot describe the actual thermodynamic evolution in state which occurs in these systems since the equation of motion used (Newton’s second law) can only describe
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Cresser, James D., and Sarah Croke. "Non-Markovian master equations with quantum trajectory unravellings." In Conference on Coherence and Quantum Optics. OSA, 2007. http://dx.doi.org/10.1364/cqo.2007.cmi49.

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Ishihara, Abraham K., and Shahar Ben-Menahem. "A Matrix WKB Approach to Feedforward and Feedback Control." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-16119.

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We apply a powerful new analytical approximation method, recently developed by the authors, to the design and analysis of feedforward and feedback control systems. This formalism employs a matrix version of the WKB expansion, which is an asymptotic approximation method familiar in quantum mechanics and classical continuum mechanics. Our matrix WKB formalism has proven remarkably useful in approximating and characterizing the long-term dynamics of systems of ODEs (both linear and nonlinear) when there exists a time scale hierarchy. In particular, the linear error dynamics encountered in the ana
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Salières, Pascal, Anne L'Huillier, and Maciej Lewenstein. "Coherence and Polarization of High Order Harmonics." In High Resolution Fourier Transform Spectroscopy. Optica Publishing Group, 1994. http://dx.doi.org/10.1364/hrfts.1994.pd2.

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The understanding of high-order harmonic generation processes has improved tremendously in the last year, with the two-step semi-classical approximation developed by Corkum and by Kulander et al. [1]. In a high-intensity low-frequency regime, the generation of harmonics occurs through the following process : the electron first tunnels out the barrier of the atomic potential lowered by the intense field. It is then accelerated in the laser field. If its trajectory encounters the nucleus, harmonics can be emitted, following the electron’s recombination to the ground state. A quantum-mechanical t
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