Relevant bibliographies by topics / Non-Hermitian Hamiltonian

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Academic literature on the topic 'Non-Hermitian Hamiltonian'

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Published: 6 September 2023

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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 generated. Usingη-pseudo-Hermiticity, the intertwining operator connecting the non-Hermitian Hamiltonians to the Hermitian counterparts is found. We have obtained a new metric tensor related to the new Hamiltonian.
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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 (April 28, 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 singularity in the spectrum of the non-Hermitian Hamiltonian may be detected as a resonance in the scattering cross section of its Hermitian counterpart. Nevertheless, just at the singular point, the equivalent Hermitian Hamiltonian becomes undetermined.
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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 (October 20, 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 effectiveness of such a protocol by applying it to physically relevant multi-spin models, showing that the effective non-Hermitian Hamiltonian drives the system to a maximally entangled stationary state. In addition, we report a new recipe to construct a physical scenario where the quantum dynamics of a physical system represented by a given non-Hermitian Hamiltonian model may be simulated. The physical implications and the broad scope potential applications of such a scheme are highlighted.
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Sharma, Preet. "𝒫𝒯-Symmetric Quantum Mechanics Basics & Zeeman Effect." Reports in Advances of Physical Sciences 04, no. 03 (September 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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Hallford, Randal, and Preet Sharma. "Non-Hermitian Hamiltonian Treatment of Stark Effect in Quantum Mechanics." Emerging Science Journal 4, no. 6 (December 1, 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 introduced to the well known Stark effect in quantum mechanics to find a condition in which the Stark effect will still be true even if a non-Hermitian Hamiltonian is used. This study completes the understanding at a fundamental level to understand the well known Stark effect. Doi: 10.28991/esj-2020-01242 Full Text: PDF
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BERMAN, GENNADY P., and ALEXANDER I. NESTEROV. "NON-HERMITIAN ADIABATIC QUANTUM OPTIMIZATION." International Journal of Quantum Information 07, no. 08 (December 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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Militello, Benedetto, and Anna Napoli. "Evanescent Wave Approximation for Non-Hermitian Hamiltonians." Entropy 22, no. 6 (June 4, 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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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 (November 20, 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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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 (April 28, 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 the energy spectrum of H is complete, Hilbert space norms 〈 ψ 1 | V | ψ 2 〉 constructed with this V are always preserved in time. With the energy eigenvalues of a real secular equation being either real or appearing in complex conjugate pairs, we thus establish the unitarity of time evolution in both cases. We also establish the unitarity of time evolution for Hamiltonians whose energy spectra are not complete. We show that when the energy eigenvalues of a Hamiltonian are real and complete, the operator V is a positive Hermitian operator, which has an associated square root operator that can be used to bring the Hamiltonian to a Hermitian form. We show that systems with -symmetric Hamiltonians obey causality. We note that Hermitian theories are ordinarily associated with a path integral quantization prescription in which the path integral measure is real, while in contrast, non-Hermitian but -symmetric theories are ordinarily associated with path integrals in which the measure needs to be complex, but in which the Euclidean time continuation of the path integral is nonetheless real. Just as the second-order Klein–Gordon theory is stabilized against transitions to negative frequencies because its Hamiltonian is positive-definite, through symmetry, the fourth-order derivative Pais–Uhlenbeck theory can equally be stabilized.
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Chen Zeng-Jun and Ning Xi-Jing. "Physical meaning of non-Hermitian Hamiltonian." Acta Physica Sinica 52, no. 11 (2003): 2683. http://dx.doi.org/10.7498/aps.52.2683.

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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.
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 non-Hermitian quadratic Hamiltonian to show that such a metric is not unique but can be uniquely defined by requiring to hermitize all elements of one of the irreducible sets defined on the set of all observables. We compare the constructed metric with specific known examples in the literature in which cases a unique choice is made.
AFRIKAANSE OPSOMMING: Ons ondersoek die implementering van n gepaste raamwerk virn nie-Hermitiese kwantumteorie. Ons beskoun nie-Hermitiese Hamilton-operator met reele eiewaardes en definieer in gepaste binneproduk ten opsigtewaarvan die operator kwasi-Hermitiese is. Die kwasi- Hermities aard van die Hamilton operator lei dan tot n stel bi-ortogonale toestande. Ons konstrueer n basistransformasie wat die linker en regter eietoestande van hierdie stel koppel. Hierdie transformasie word dan gebruik omn nuwe binneproduk op die Hilbert-ruimte te definieer. Die oorspronklike nie-HermitieseHamilton-operator is danHermitiesmet betrekking tot hierdie nuwe binneproduk. Ons gebruik die nie-Hermitiese kwadratieseHamilton-operator omte toon dat hierdie metriek nie uniek is nie, maar wel uniek bepaal kan word deur verder te vereis dat dit al die elemente van n onherleibare versameling operatoreHermitiseer. Ons vergelyk hierdie konstruksiemet die bekende voorbeelde in die literatuur en toon dat diemetriek in beide gevalle uniek bepaal kan word.
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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 expressed as linear and quadratic combinations of the generators of the su(1; 1) Lie algebra, we construct [2] Hermitian partners in the same similarity class. Alongside, metrics with respect to which the original Hamiltonians are Hermitian are also constructed, allowing to assign meaning to a large class of non-Hermitian Hamiltonians possessing real spectra. The finding of exact results to establish the physical acceptability of other non-Hermitian models may be pursued by other means, especially if the system of interest cannot be expressed in terms of Lie algebraic elements. We also employ [3] a representation of the canonical commutation relations for position and momentum operators in terms of real-valued functions and a noncommutative product rule of differential form. Besides exact solutions, we also compute in a perturbative fashion metrics and isospectral partners for systems of physical interest. Classically, our efforts were concentrated on integrable models presenting PT - symmetry. Because the latter can also establish the reality of energies in classical systems described by Hamiltonian functions, we search for new families of nonlinear differential equations for which the presence of hidden symmetries allows one to assemble exact solutions. We use [4] the Painleve test to check whether deformations of integrable systems preserve integrability. Moreover we compare [5] integrable deformed models, which are thus likely to possess soliton solutions, to a broader class of systems presenting compacton solutions. Finally we study [6] the pole structure of certain real valued nonlinear integrable systems and establish that they behave as interacting particles whose motion can be extended to the complex plane in a PT -symmetric way.
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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.
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 speci cally on obtaining the real and discrete energy spectrum. Various methods for solving this problematic Schr odinger equation will be considered. After starting with perturbation theory, we will move on to numerical methods. Three di erent categories of methods will be discussed. First there is the shooting method based on a Runge-Kutta solver. Next, we investigate various implementations of the spectral method. Finally, we will look at the Riccati-Pad e method, which is a numerical implemented analytical method. PT -symmetric potentials need to be solved along a contour in the complex plane. We will propose modi cations to the numerical methods to handle this. After solving the widely documented PT -symmetric Hamiltonian H = p2 􀀀(ix)N with these methods, we give a discussion and comparison of the obtained results. Finally, we solve another PT -symmetric potential, illustrating the use of paths in the complex plane to obtain a real and discrete spectrum and their in uence on the results.
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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, superconducting wires and circuits. The objective of this thesis is to extend the iterative method of solving Schrodinger equation used for an harmonic oscillator systems to Hamiltonians with PT-symmetric potentials. An important aspect of this approach is the high accuracy of eigenvalues and the fast convergence. Our method is a combination of Hill determinant method [8] and the power series expansion. eigenvalues and the fast convergence. One can transform the Schrodinger equation into a secular equation by using a trial wave function. A recursion structure can be obtained using the secular equation, which leads to accurate eigenvalues. Energy values approach to exact ones when the number of iterations is increased. We obtained eigenvalues for a set of PT-symmetric Hamiltonians.
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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. Cham: 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, 287–322. Boston, MA: 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, 245–54. New York, NY: 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, 93–100. Boston, MA: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-0971-0_8.

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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, 83–95. Cham: 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, N. Maggiore, M. Sarandy, S. Sorella, Steven Duplij, et al. "Non-Hermitian Hamiltonians." In Concise Encyclopedia of Supersymmetry, 267. Dordrecht: 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, 341–61. Berlin, Heidelberg: 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, 83–99. Singapore: 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, 411–26. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20087-9_20.

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Zelaya, Kevin, Sara Cruz y Cruz, and Oscar Rosas-Ortiz. "On the Construction of Non-Hermitian Hamiltonians with All-Real Spectra Through Supersymmetric Algorithms." In Trends in Mathematics, 283–92. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53305-2_18.

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MOGHADDAM, AMIR, JON LINKS, and YAO-ZHONG ZHANG. "EXACTLY SOLVABLE, NON-HERMITIAN BCS HAMILTONIAN." In Symmetries and Groups in Contemporary Physics, 627–30. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814518550_0091.

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Conference papers on the topic "Non-Hermitian Hamiltonian"

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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, A. Schumer, A. U. Hassan, Q. Zhong, S. Rotter, P. L. LiKamWa, D. N. Christodoulides, and M. Khajavikhan. "Dynamics of Chiral State Transfer in the Vicinity of a Non-Hermitian Singularity." In CLEO: QELS_Fundamental Science. Washington, D.C.: 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. Washington, D.C.: 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. Washington, D.C.: OSA, 2018. http://dx.doi.org/10.1364/cleo_qels.2018.fm2q.4.

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Kleefeld, Frieder. "Consistent relativistic Quantum Theory for systems/particles described by non-Hermitian Hamiltonians and Lagrangians." In HADRON PHYSICS: Effective Theories of Low Energy QCD Second International Workshop on Hadron Physics. AIP, 2003. http://dx.doi.org/10.1063/1.1570583.

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