# Wave-packet evolution in non-Hermitian quantum systems

@article{Graefe2011WavepacketEI, title={Wave-packet evolution in non-Hermitian quantum systems}, author={Eva-Maria Graefe and Roman Schubert}, journal={Physical Review A}, year={2011}, volume={83} }

The quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical limit ({h_bar}/2{pi}){yields}0 this yields the non-Hermitian analog of the Ehrenfest theorem for the dynamics of observable expectation values. The lack of Hermiticity reveals the importance of the complex structure on the classical phase space: The resulting equations of motion are coupled to an equation of motion for the phase-space metric - a…

## 42 Citations

Classical and quantum dynamics in the (non-Hermitian) Swanson oscillator

- Physics
- 2014

The non-Hermitian quadratic oscillator known as the Swanson oscillator is one of the popular PT-symmetric model systems. Here a full classical description of its dynamics is derived using recently…

Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems

- PhysicsPhysical Review B
- 2020

Berry phases strongly affect the properties of crystalline materials, giving rise to modifications of the semiclassical equations of motion that govern wave-packet dynamics. In non-Hermitian systems,…

Non-Hermitian Schrödinger dynamics with Hagedorn’s wave packets

- Mathematics, Physics
- 2017

Hagedorn wave packets form an orthonormal basis of the L2-functions and are known solutions of the semiclassical Schrodinger equation with quadratic Hamiltonians. In this thesis we analyse their…

Matrix Algebras in Non-Hermitian Quantum Mechanics

- Mathematics, Physics
- 2010

In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schrodinger's picture of quantum dynamics. Here it is shown in both…

NON-HERMITIAN QUANTUM DYNAMICS OF A TWO-LEVEL SYSTEM AND MODELS OF DISSIPATIVE ENVIRONMENTS

- Physics
- 2013

We consider a non-Hermitian Hamiltonian in order to effectively describe a two-level system (TLS) coupled to a generic dissipative environment. The total Hamiltonian of the model is obtained by…

Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay

- PhysicsInternational Journal of Modern Physics B
- 2018

The Wigner–Weyl transform and phase space formulation of a density matrix approach are applied to a non-Hermitian model which is quadratic in positions and momenta. We show that in the presence of a…

The density matrix in the non-Hermitian approach to open quantum system dynamics

- Physics
- 2019

In this paper we review an approach to the dynamics of open quantum systems based of non-Hermitian Hamiltonians. Non-Hermitian Hamiltonians arise naturally when one wish to study a subsystem…

Embedding quantum systems with a non-conserved probability in classical environments

- Physics, MathematicsTheoretical Chemistry Accounts
- 2015

Quantum systems with a non-conserved probability can be described by means of non-Hermitian Hamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be…

Berry connection induced anomalous drift velocity in non-Hermitian systems

- Physics
- 2020

Berry phases strongly affect the properties of crystalline materials, giving rise to modifications of the semiclassical equations of motion that govern wave-packet dynamics. In non-Hermitian systems,…

Geometry and Dynamics of Gaussian Wave Packets and their Wigner Transforms

- Physics
- 2016

We find a relationship between the dynamics of the Gaussian wave packet and the dynamics of the corresponding Gaussian Wigner function from the Hamiltonian/symplectic point of view. The main result…

## References

SHOWING 1-10 OF 41 REFERENCES

Classical limit of non-Hermitian quantum dynamics—a generalized canonical structure

- Physics, Mathematics
- 2010

We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by…

The classical limit for quantum mechanical correlation functions

- Physics
- 1974

For quantum systems of finitely many particles as well as for boson quantum field theories, the classical limit of the expectation values of products of Weyl operators, translated in time by the…

Quantum-classical correspondence for a non-Hermitian Bose-Hubbard dimer

- Physics
- 2010

We investigate the many-particle and mean-field correspondence for a non-Hermitian N-particle Bose-Hubbard dimer where a complex on-site energy describes an effective decay from one of the modes.…

A simple nonlinear dissipative quantum evolution equation

- Physics
- 1981

The author has considered a nonlinear dissipative evolution equation that generalises the Schrodinger equation. In the corresponding evolution all the stationary states of the usual Schrodinger…

Semiclassical spreading of quantum wave packets and applications near unstable fixed points of the classical flow

- Physics
- 1997

Precise semiclassical estimates for the spreading of quantum wave packets are derived, when the initial wave packet is in a coherent state. We find asymptotics for the quantum evolution of coherent…

Time‐dependent approach to semiclassical dynamics

- Physics
- 1975

In this paper we develop a new approach to semiclassical dynamics which exploits the fact that extended wavefunctions for heavy particles (or particles in harmonic potentials) may be decomposed into…

Quantum noise and self-sustained radiation of PT-symmetric systems.

- PhysicsPhysical review letters
- 2010

This work shows that microreversibility-breaking quantum noise turns PT-symmetric systems into self-sustained sources of radiation, which distinguishes them from ordinary, Hermitian quantum systems.

Fractal Weyl laws for quantum decay in dynamical systems with a mixed phase space.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

It is shown that resonances in open quantum systems can follow a modified fractal Weyl law, even when their classical dynamics is not globally chaotic but also contains domains of regular motion, and connected to emerging quantum-to-classical correspondence.

Gaussian-based techniques for quantum propagation from the time-dependent variational principle: Formulation in terms of trajectories of coupled classical and quantum variables.

- PhysicsThe Journal of chemical physics
- 2008

In this article, two coherent-state based methods of quantum propagation, namely, coupled coherent states (CCS) and Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH), are put on the…