Wave-packet evolution in non-Hermitian quantum systems

Graefe, Eva-Maria; Schubert, Roman

doi:10.1103/physreva.83.060101

Cited by 49 publications

(89 citation statements)

References 34 publications

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“…The non-normalized density matrixΩ(t) of the composite system with nonHermitian Hamiltonian H obeys the equation of motion [47] ∂ ∂tΩ In order to obtain the quantum-classical limit of Eq. (3) a rigorous procedure, which is based on the partial Wigner representation of the dynamics and the linear expansion in µ, can be followed.…”

Section: Non-hermitian Quantum Mechanics In a Classical Bathmentioning

confidence: 99%

“…The theoretical investigations are also undergoing rapid developments: non-Hermitian quantum mechanics has been investigated within a relativistic framework [31] and it has been adopted by various researchers as a means to describe open quantum systems [32][33][34][35][36][37][38][39][40][41][42]. Moreover, it seems that a few theoretical studies have been dedicated to the statistical mechanics and dynamics of systems with non-Hermitian Hamiltonians [43][44][45][46][47][48][49][50][51][52][53][54].…”

Section: Introductionmentioning

confidence: 99%

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

Sergi

2015

Theor Chem Acc

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Quantum systems with a non-conserved probability can be described by means of non-HermitianHamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and heavy masses is treated. A classical limit over the heavy coordinates is taken in order to embed the non-unitary dynamics of the subsystem in a classical environment. Such a classical environment, in turn, acts as an additional source of dissipation (or noise), beyond that represented by the non-unitary evolution. The non-Hermitian dynamics of a Heisenberg two-spin chain, with the spins independently coupled to harmonic oscillators, is considered in order to illustrate the formalism.

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Section: Non-hermitian Quantum Mechanics In a Classical Bathmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Sergi

2015

Theor Chem Acc

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“…It has been recently argued in [9] that a quasiclassical description of Bloch oscillations in the non-Hermitian case is of little use. Here, however, we show that the classical dynamics recently developed in [21][22][23][24] as a counterpart of non-Hermitian quantum dynamics, is capable of describing the main features of Bloch oscillations as well in the non-Hermitian case, as long as only a single Bloch band is involved in the dynamics (a constraint that also holds in the Hermitian case).…”

Section: Introductionmentioning

confidence: 80%

Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices

2016

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Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is based on a generalised non-Hermitian phase space dynamics developed recently. Applications to a single-band tight-binding system demonstrate that many features of the quantum dynamics can be understood from this classical description qualitatively and even quantitatively. Two non-Hermitian and PT-symmetric examples are studied, a Hatano-Nelson lattice with real coupling constants and a system with purely imaginary couplings, both for initially localised states in space or in momentum. It is shown that the time-evolution of the norm of the wave packet and the expectation values of position and momentum can be described in a classical picture.

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“…It might seem natural to assume the metric to be given by the standard euclidean metric G = I [4]. As has been shown in [5,6], however, starting from the quantum dynamics in the semiclassical limit, G is itself time dependent. The time evolution of the metric is governed by the dynamical equatioṅ…”

Section: Classical Metriplectic Dynamicsmentioning

confidence: 99%

“…A first step towards classical non-Hermitian dynamics has been made by the authors in [4,5]. The interesting complex structure of the resulting metriplectic flow in phase space was revealed in [6].…”

Section: Introductionmentioning

confidence: 99%

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

Graefe¹,

Korsch²,

Rushton³

et al. 2015

J. Phys. A: Math. Theor.

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Abstract. The non-Hermitian quadratic oscillator known as Swanson oscillator is one of the popular P T -symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine the classical symplectic flow for Hermitian systems with a dissipative metric flow for the anti-Hermitian part. Closed form expressions for the metric and phasespace trajectories are presented which are found to be periodic in time. Since the Hamiltonian is only quadratic the classical dynamics exactly describes the quantum dynamics of Gaussian wave packets. It is shown that the classical metric and trajectories as well as the quantum wave functions can diverge in finite time even though the P T -symmetry is unbroken, i.e., the eigenvalues are purely real.

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Wave-packet evolution in non-Hermitian quantum systems

Cited by 49 publications

References 34 publications

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

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

Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices

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

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