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A numerical method is developed to solve the time-dependent Dirac equation in cylindrical coordinates for 3-D axisymmetric systems. The time evolution is treated by a splitting scheme in coordinate space using alternate direction iteration,…

Computational Physics · Physics 2015-04-03 François Fillion-Gourdeau , Emmanuel Lorin , André D. Bandrauk

Parity-time ($\mathcal{PT}$) symmetry plays an important role both in non-Hermitian and topological systems. In non-Hermitian systems $\mathcal{PT}$ symmetry can lead to an entirely real energy spectrum, while in topological systems…

Mesoscale and Nanoscale Physics · Physics 2019-12-18 W. B. Rui , Moritz M. Hirschmann , Andreas P. Schnyder

The exceptional point, known as the non-Hermitian degeneracy, has special topological structure, leading to various counterintuitive phenomena and novel applications, which are refreshing our cognition of quantum physics. One particularly…

Quantum Physics · Physics 2021-05-05 Wenquan Liu , Yang Wu , Chang-Kui Duan , Xing Rong , Jiangfeng Du

We discuss how introducing an equilibrium frame, in which a given Hamiltonian has balanced loss and gain terms, can reveal PT symmetry hidden in non-Hermitian Hamiltonians of dissipative systems. Passive PT-symmetric Hamiltonians, in which…

Quantum Physics · Physics 2021-08-16 Grzegorz Chimczak , Anna Kowalewska-Kudłaszyk , Ewelina Lange , Karol Bartkiewicz

To find and realize the optimal evolution between two states is significant both in theory and application. In quantum mechanics, the minimal evolution is bounded by the gap between the largest and smallest eigenvalue of the Hamiltonian. In…

Quantum Physics · Physics 2013-04-29 Chao Zheng , Liang Hao , Gui Lu Long

The physics of systems that cannot be described by a Hermitian Hamiltonian, has been attracting a great deal of attention in recent years, motivated by their nontrivial responses and by a plethora of applications for sensing, lasing, energy…

Optics · Physics 2021-03-16 Alex Krasnok , Nikita Nefedkin , Andrea Alu

A $\mathcal{PT}$-symmetric nonlinear Schr\"odinger dimer is a two-site discrete nonlinear Schr\"odinger equation with one site losing and the other one gaining energy at the same rate. In this paper, two four-parameter families of cubic…

Exactly Solvable and Integrable Systems · Physics 2015-09-02 I. V. Barashenkov , D. E. Pelinovsky , P. Dubard

We experimentally demonstrate an unambiguous quantum state discrimination of two qubit states under a non-Hermitian Hamiltonian with parity-time-reversal ($\mathcal{PT}$) symmetry in a single trapped $^{40}$Ca$^+$ ion. We show that any two…

Quantum Physics · Physics 2025-03-03 Chenhao Zhu , Tingting Shi , Liangyu Ding , Zhiyue Zheng , Xiang Zhang , Wei Zhang

We introduce a class of PT-symmetric systems which include mutually matched nonlinear loss and gain (inother words, a class of PT-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system…

Mathematical Physics · Physics 2015-05-27 Andrey E. Miroshnichenko , Boris A. Malomed , Yuri S. Kivshar

In this work we intend to study a class of time-dependent quantum systems with non-Hermitian Hamiltonians, particularly those whose Hermitian counterpart are important for the comprehension of posed problems in quantum optics and quantum…

Quantum Physics · Physics 2007-05-23 A. de Souza Dutra , M. B. Hott , V. G. C. S dos Santos

A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…

Quantum Physics · Physics 2009-11-11 V. G. Kupriyanov , S. L. Lyakhovich , A. A. Sharapov

Within the framework of the recently proposed formalism using non-hermitean Hamiltonians constrained merely by their PT invariance we describe a new exactly solvable family of the harmonic-oscillator-like potentials with non-equidistant…

Quantum Physics · Physics 2009-10-31 Miloslav Znojil

This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition $H^\dagger=H$ on the Hamiltonian, where $\dagger$ represents the mathematical operation of complex conjugation and matrix…

Quantum Physics · Physics 2009-10-31 Carl Bender , Stefan Boettcher , Peter Meisinger

We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with…

Quantum Physics · Physics 2017-06-19 Boubakeur Khantoul , A. Bounames , M. Maamache

Non-Hermiticity in quantum Hamiltonians leads to nonunitary time evolution and possibly complex energy eigenvalues, which can lead to a rich phenomenology with no Hermitian counterpart. In this work, we study the dynamics of an exactly…

Quantum Physics · Physics 2023-10-25 Karin Sim , Nicolò Defenu , Paolo Molignini , R. Chitra

This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…

Quantum Physics · Physics 2013-10-25 Gerald I. Kerley

The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control.…

We study the dissipative dynamics of a one-dimensional bosonic system described in terms of the bipartite Bose-Hubbard model with alternating gain and loss. This model exhibits the $\mathcal{PT}$ symmetry under some specific conditions and…

Quantum Gases · Physics 2023-03-07 Cătălin Paşcu Moca , Doru Sticlet , Balázs Dóra , Gergely Zaránd

This work studies a $\mathcal{PT}$-symmetric non-Hermitian spin--boson model, consisting of a non-Hermitian two-level system coupled to a continuous bosonic bath. The static properties of the system are analyzed through a projection method…

Quantum Physics · Physics 2025-12-24 Yong-Xin Zhang , Qing-Hu Chen

Parity-time ($\mathcal{PT}$) symmetric systems are classical, gain-loss systems whose dynamics are governed by non-Hermitian Hamiltonians with exceptional-point (EP) degeneracies. The eigenvalues of a $\mathcal{PT}$-symmetric Hamiltonian…

Quantum Physics · Physics 2021-08-27 Kaustubh S. Agarwal , Yogesh N. Joglekar