Relevant bibliographies by topics / Non-Hermitian Hamiltonian

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Academic literature on the topic 'Non-Hermitian Hamiltonian'

Author: Grafiati
Published: 6 September 2023
Last updated: 19 July 2025

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Journal articles on the topic "Non-Hermitian Hamiltonian"

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Yeşiltaş, Özlem. "Non-Hermitian Dirac Hamiltonian in Three-Dimensional Gravity and Pseudosupersymmetry." Advances in High Energy Physics 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/484151.

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The Dirac Hamiltonian in the(2+1)-dimensional curved space-time has been studied with a metric for an expanding de Sitter space-time which is two spheres. The spectrum and the exact solutions of the time dependent non-Hermitian and angle dependent Hamiltonians are obtained in terms of the Jacobi and Romanovski polynomials. Hermitian equivalent of the Hamiltonian obtained from the Dirac equation is discussed in the frame of pseudo-Hermiticity. Furthermore, pseudosupersymmetric quantum mechanical techniques are expanded to a curved Dirac Hamiltonian and a partner curved Dirac Hamiltonian is gene
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Samsonov, Boris F. "Hermitian Hamiltonian equivalent to a given non-Hermitian one: manifestation of spectral singularity." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (2013): 20120044. http://dx.doi.org/10.1098/rsta.2012.0044.

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One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equivalent to the given non-Hermitian one is found. As a result, the corresponding scattering matrix and cross section are given explicitly. It is demonstrated that the possible presence of a spectral singu
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Grimaudo, Roberto, Antonino Messina, Alessandro Sergi, Nikolay V. Vitanov, and Sergey N. Filippov. "Two-Qubit Entanglement Generation through Non-Hermitian Hamiltonians Induced by Repeated Measurements on an Ancilla." Entropy 22, no. 10 (2020): 1184. http://dx.doi.org/10.3390/e22101184.

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In contrast to classical systems, actual implementation of non-Hermitian Hamiltonian dynamics for quantum systems is a challenge because the processes of energy gain and dissipation are based on the underlying Hermitian system–environment dynamics, which are trace preserving. Recently, a scheme for engineering non-Hermitian Hamiltonians as a result of repetitive measurements on an ancillary qubit has been proposed. The induced conditional dynamics of the main system is described by the effective non-Hermitian Hamiltonian arising from the procedure. In this paper, we demonstrate the effectivene
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Sharma, Preet. "𝒫𝒯-Symmetric Quantum Mechanics Basics & Zeeman Effect". Reports in Advances of Physical Sciences 04, № 03 (2020): 2050006. http://dx.doi.org/10.1142/s2424942420500061.

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The non-Hermitian aspect of Quantum Mechanics has been of great interest recently. There have been numerous studies on non-Hermitian Hamiltonians written for natural processes. Some studies have even expressed the hydrogen atom in a non-Hermitian basis. In this paper, the principles of non-Hermitian quantum mechanics are applied to the time independent perturbation theory and compared with the Zeeman effect. Here, we have also shown the condition under which the Zeeman Effect results will still be true even though the Hamiltonian taken into consideration is non-Hermitian.
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Rottoli, Federico, Michele Fossati, and Pasquale Calabrese. "Entanglement Hamiltonian in the non-Hermitian SSH model." Journal of Statistical Mechanics: Theory and Experiment 2024, no. 6 (2024): 063102. http://dx.doi.org/10.1088/1742-5468/ad4860.

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Abstract Entanglement Hamiltonians provide the most comprehensive characterisation of entanglement in extended quantum systems. A key result in unitary quantum field theories is the Bisognano-Wichmann theorem, which establishes the locality of the entanglement Hamiltonian. In this work, our focus is on the non-Hermitian Su-Schrieffer-Heeger (SSH) chain. We study the entanglement Hamiltonian both in a gapped phase and at criticality. In the gapped phase we find that the lattice entanglement Hamiltonian is compatible with a lattice Bisognano-Wichmann result, with an entanglement temperature line
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Hallford, Randal, and Preet Sharma. "Non-Hermitian Hamiltonian Treatment of Stark Effect in Quantum Mechanics." Emerging Science Journal 4, no. 6 (2020): 427–35. http://dx.doi.org/10.28991/esj-2020-01242.

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The Non-Hermitian aspect of Quantum Mechanics has been of great interest recently. There have been numerous studies on non-Hermitian Hamiltonians written for natural processes. Some studies have even expressed the hydrogen atom in a non-Hermitian basis. In this paper the principles of non-Hermitian quantum mechanics is applied to both the time independent perturbation theory and to the time dependant theory to calculate the Stark effect. The principles of spherical harmonics has also been used to describe the development in the non-Hermitian case. Finally, the non-Hermitian aspect has been int
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BERMAN, GENNADY P., and ALEXANDER I. NESTEROV. "NON-HERMITIAN ADIABATIC QUANTUM OPTIMIZATION." International Journal of Quantum Information 07, no. 08 (2009): 1469–78. http://dx.doi.org/10.1142/s0219749909005961.

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We propose a novel non-Hermitian adiabatic quantum optimization algorithm. One of the new ideas is to use a non-Hermitian auxiliary "initial" Hamiltonian that provides an effective level repulsion for the main Hamiltonian. This effect enables us to develop an adiabatic theory which determines ground state much more efficiently than Hermitian methods.
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SINHA, A., and P. ROY. "DARBOUX TRANSFORMATION FOR THE ONE-DIMENSIONAL STATIONARY DIRAC EQUATION WITH NON-HERMITIAN INTERACTION." International Journal of Modern Physics A 21, no. 28n29 (2006): 5807–22. http://dx.doi.org/10.1142/s0217751x0603312x.

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The Darboux algorithm is applied to an exactly solvable one-dimensional stationary Dirac equation, with non-Hermitian, pseudoscalar interaction V0(x). This generates a hierarchy of exactly solvable Dirac Hamiltonians, [Formula: see text], defined by new non-Hermitian interactions V1(x), which are also pseudoscalar. It is shown that [Formula: see text] are isospectral to the initial Hamiltonian h0, except for certain missing states.
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Militello, Benedetto, and Anna Napoli. "Evanescent Wave Approximation for Non-Hermitian Hamiltonians." Entropy 22, no. 6 (2020): 624. http://dx.doi.org/10.3390/e22060624.

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The counterpart of the rotating wave approximation for non-Hermitian Hamiltonians is considered, which allows for the derivation of a suitable effective Hamiltonian for systems with some states undergoing decay. In the limit of very high decay rates, on the basis of this effective description we can predict the occurrence of a quantum Zeno dynamics, which is interpreted as the removal of some coupling terms and the vanishing of an operatorial pseudo-Lamb shift.
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Mannheim, Philip D. "PT symmetry as a necessary and sufficient condition for unitary time evolution." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (2013): 20120060. http://dx.doi.org/10.1098/rsta.2012.0060.

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While Hermiticity of a time-independent Hamiltonian leads to unitary time evolution, in and of itself, the requirement of Hermiticity is only sufficient for unitary time evolution. In this paper, we provide conditions that are both necessary and sufficient. We show that symmetry of a time-independent Hamiltonian, or equivalently, reality of the secular equation that determines its eigenvalues, is both necessary and sufficient for unitary time evolution. For any -symmetric Hamiltonian H , there always exists an operator V that relates H to its Hermitian adjoint according to V HV −1 = H † . When
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Dissertations / Theses on the topic "Non-Hermitian Hamiltonian"

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Musumbu, Dibwe Pierrot. "The metric for non-Hermitian Hamiltonians : a case study." Thesis, Stellenbosch : Stellenbosch University, 2006. http://hdl.handle.net/10019.1/17403.

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Thesis (MSc)--University of Stellenbosch, 2006.<br>ENGLISH ABSTRACT: We are studying a possible implementation of an appropriate framework for a proper non- Hermitian quantum theory. We present the case where for a non-Hermitian Hamiltonian with real eigenvalues, we define a new inner product on the Hilbert space with respect to which the non-Hermitian Hamiltonian is Quasi-Hermitian. The Quasi-hermiticity of the Hamiltonian introduces the bi-orthogonality between the left-hand eigenstates and the right-hand eigenstates, in which case the metric becomes a basis transformation. We use the n
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Assis, Paulo. "Non-Hermitian Hamiltonians in field theory." Thesis, City University London, 2009. http://openaccess.city.ac.uk/2118/.

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This thesis is centred around the role of non-Hermitian Hamiltonians in Physics both at the quantum and classical levels. In our investigations of two-level models we demonstrate [1] the phenomenon of fast transitions developed in the PT -symmetric quantum brachistochrone problem may in fact be attributed to the non-Hermiticity of evolution operator used, rather than to its invariance under PT operation. Transition probabilities are calculated for Hamiltonians which explicitly violate PT -symmetry. When it comes to Hilbert spaces of infinite dimension, starting with non-Hermitian Hamiltonians
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Wessels, Gert Jermia Cornelus. "A numerical and analytical investigation into non-Hermitian Hamiltonians." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/2894.

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Thesis (MSc (Physical and Mathematical Analysis))--University of Stellenbosch, 2009.<br>In this thesis we aim to show that the Schr odinger equation, which is a boundary eigenvalue problem, can have a discrete and real energy spectrum (eigenvalues) even when the Hamiltonian is non-Hermitian. After a brief introduction into non-Hermiticity, we will focus on solving the Schr odinger equation with a special class of non-Hermitian Hamiltonians, namely PT - symmetric Hamiltonians. PT -symmetric Hamiltonians have been discussed by various authors [1, 2, 3, 4, 5] with some of them focusing spec
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Wijewardena, Udagamge. "Iterative method of solving schrodinger equation for non-Hermitian, pt-symmetric Hamiltonians." DigitalCommons@Robert W. Woodruff Library, Atlanta University Center, 2016. http://digitalcommons.auctr.edu/dissertations/3194.

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PT-symmetric Hamiltonians proposed by Bender and Boettcher can have real energy spectra. As an extension of the Hermitian Hamiltonian, PT-symmetric systems have attracted a great interest in recent years. Understanding the underlying mathematical structure of these theories sheds insight on outstanding problems of physics. These problems include the nature of Higgs particles, the properties of dark matter, the matter-antimatter asymmetry in the universe, and neutrino oscillations. Furthermore, PT-phase transition has been observed in lasers, optical waveguides, microwave cavities, superconduct
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Panda, Animesh. "Quantum oscillation in band insulators and properties of non-equilibrium steady states in disordered insulators." Thesis, 2023. https://etd.iisc.ac.in/handle/2005/6203.

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Starting with the experiment on Kondo insulator SmB6 , which shows 1/B-periodic oscillations despite the absence of gapless electronic excitations in bulk, the candidate insulators showing quantum oscillation (QO) are on the rise. But this is contrary to our conventional understanding that we need a Fermi surface to have QO. So an obvious question to ask is, ‘How can insulators show QO?’. If there is QO, then which physical quantities show QO, and what is the physical reason behind their origin? In the absence of a Fermi surface, what determines the frequency of these QO? In search of answers,
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Suen, Gwo-Hong. "The formulation of non-Hermitian PT-symmetric Hamiltonians and pseudo-Hermiticity." 2007. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-2607200711424900.

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Books on the topic "Non-Hermitian Hamiltonian"

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Bagarello, Fabio, Roberto Passante, and Camillo Trapani, eds. Non-Hermitian Hamiltonians in Quantum Physics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31356-6.

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Bagarello, Fabio, Roberto Passante, and Camillo Trapani. Non-Hermitian Hamiltonians in Quantum Physics: Selected Contributions from the 15th International Conference on Non-Hermitian Hamiltonians in Quantum ... May 2015. Springer, 2018.

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Bagarello, Fabio, Roberto Passante, and Camillo Trapani. Non-Hermitian Hamiltonians in Quantum Physics: Selected Contributions from the 15th International Conference on Non-Hermitian Hamiltonians in Quantum ... May 2015. Springer, 2016.

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Bagarello, Fabio, Roberto Passante, and Camillo Trapani. Non-Hermitian Hamiltonians in Quantum Physics: Selected Contributions from the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, Palermo, Italy, 18-23 May 2015. Springer London, Limited, 2016.

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Book chapters on the topic "Non-Hermitian Hamiltonian"

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Faisal, Farhad H. M. "Non-Hermitian Hamiltonian Theory of Multiphoton Transitions." In Theory of Multiphoton Processes. Springer US, 1987. http://dx.doi.org/10.1007/978-1-4899-1977-9_11.

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Ergun, Ebru. "On the Eigenvalues of a Non-Hermitian Hamiltonian." In Dynamical Systems and Methods. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0454-5_13.

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Cambiaggio, M. C., and J. Dukelsky. "Variational Approximation to the Non-Hermitian Dyson Boson Hamiltonian." In Condensed Matter Theories. Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-0971-0_8.

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Yang, Fu-Bao, and Ji-Ping Huang. "Geometric Phases in Particle Diffusion with Non-Hermitian Hamiltonian Structures." In Diffusionics. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-0487-3_16.

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AbstractGeometric phases in particle diffusion systems offer a different understanding beyond traditional Brownian motion and Fick’s laws. Here we introduce a unique structure composed of two rings moving in opposite directions and a stationary intermediate layer, which plays multifunctional roles in controlling particle diffusion. Numerical simulations using COMSOL Multiphysics validate the theoretical framework and provide deeper insights into the behavior of geometric phase. We also describe a bilayer particle-diffusion cloak, illustrating its simple design and adaptable control mechanisms. This system has potential applications in industries like healthcare and environmental management, thus expanding the understanding of the geometric phase and offering insights for the design of particle-diffusion metamaterials.
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Virdi, Jasvinder Singh. "Complex Invariants Corresponding Non-hermitian $$\mathcal{P}\mathcal{T}$$-Symmetric Hamiltonian." In Springer Proceedings in Physics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-66874-6_51.

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Bagarello, Fabio, Francesco Gargano, Margherita Lattuca, Roberto Passante, Lucia Rizzuto, and Salvatore Spagnolo. "Exceptional Points in a Non-Hermitian Extension of the Jaynes-Cummings Hamiltonian." In Springer Proceedings in Physics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31356-6_6.

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Aoyama, Hideaki, Anatoli Konechny, V. Lemes, et al. "Non-Hermitian Hamiltonians." In Concise Encyclopedia of Supersymmetry. Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_350.

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Bender, Carl M., and Dorje C. Brody. "Optimal Time Evolution for Hermitian and Non-Hermitian Hamiltonians." In Time in Quantum Mechanics II. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03174-8_12.

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Miyaoka, Reiko. "Hamiltonian Non-displaceability of the Gauss Images of Isoprametric Hypersurfaces (A Survey)." In Hermitian–Grassmannian Submanifolds. Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-5556-0_8.

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Znojil, Miloslav. "On Some Aspects of Unitary Evolution Generated by Non-Hermitian Hamiltonians." In Integrability, Supersymmetry and Coherent States. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20087-9_20.

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Conference papers on the topic "Non-Hermitian Hamiltonian"

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Rivero, Jose D. H., Courtney Fleming, Bingkun Qi, Liang Feng, and Li Ge. "Robust symmetry-free zero modes in non-Hermitian systems." In CLEO: Fundamental Science. Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_fs.2024.fth4d.2.

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Cheng, Dali, Eran Lustig, Kai Wang, and Shanhui Fan. "Band structure measurements in multi-dimensional synthetic frequency lattices." In CLEO: Fundamental Science. Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_fs.2024.fth4d.6.

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We experimentally demonstrate a method to fully measure multi-dimensional band structures in synthetic frequency dimensions by introducing a gauge potential into the lattice Hamiltonian. We use this method to study non-Hermitian topology in high dimensions.
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Celardo, G. L., A. Biella, G. G. Giusteri, F. Mattiotti, Y. Zhang, and L. Kaplan. "Superradiance, disorder, and the non-Hermitian Hamiltonian in open quantum systems." In LIGHT AND ITS INTERACTIONS WITH MATTER. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4899219.

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Nasari, H., G. Lopez-Galmiche, H. E. Lopez-Aviles, et al. "Dynamics of Chiral State Transfer in the Vicinity of a Non-Hermitian Singularity." In CLEO: QELS_Fundamental Science. Optica Publishing Group, 2022. http://dx.doi.org/10.1364/cleo_qels.2022.fm5b.7.

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The parametric steering of a non-Hermitian Hamiltonian on closed loops excluding the exceptional point is studied. It is shown that a combination of topology and shape of the Riemann surfaces governs the topological state transfer.
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Zloshchastiev, Konstantin G. "Non-Hermitian Hamiltonian approach for electromagnetic wave propagation and dissipation in dielectric media." In 2016 9th International Kharkiv Symposium on Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves (MSMW). IEEE, 2016. http://dx.doi.org/10.1109/msmw.2016.7538192.

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Chen, Zihao, Yao Zhou, and Jung-Tsung Shen. "Breakdown of Non-Hermitian Hamiltonian for Correlated Multi-photon Transport Due to Reservoir-induced Correlation Changes." In CLEO: QELS_Fundamental Science. OSA, 2019. http://dx.doi.org/10.1364/cleo_qels.2019.ftu3b.6.

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Kocharovsky, V. V., Vl V. Kocharovsky, S. A. Litvak, I. A. Shereshevsky, and E. A. Derishev. "Nonunitary evolution of the dressed states coupled with a continuum: possible optical verification of the true non-Hermitian Hamiltonian." In International Conference on Coherent and Nonlinear Optics, edited by A. L. Andreev, Olga A. Kocharovskaya, and Paul Mandel. SPIE, 1996. http://dx.doi.org/10.1117/12.239484.

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BENDER, CARL M. "NON-HERMITIAN HAMILTONIANS HAVING REAL SPECTRA." In Proceedings of the Sixth Workshop. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812778352_0025.

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HO, CHOON-LIN. "PREPOTENTIAL APPROACH TO EXACT AND QUASI-EXACT SOLVABILITIES OF HERMITIAN AND NON-HERMITIAN HAMILTONIANS." In Statistical Physics, High Energy, Condensed Matter and Mathematical Physics - The Conference in Honor of C. N. Yang'S 85th Birthday. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812794185_0055.

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Cerjan, Alexander, Meng Xiao, Luqi Yuan, and Shanhui Fan. "Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges." In CLEO: QELS_Fundamental Science. OSA, 2018. http://dx.doi.org/10.1364/cleo_qels.2018.fm2q.4.

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