Search results for "non-Hermitian Hamiltonians"
showing 7 items of 7 documents
Bicoherent-State Path Integral Quantization of a non-Hermitian Hamiltonian
2020
We introduce, for the first time, bicoherent-state path integration as a method for quantizing non-hermitian systems. Bicoherent-state path integrals arise as a natural generalization of ordinary coherent-state path integrals, familiar from hermitian quantum physics. We do all this by working out a concrete example, namely, computation of the propagator of a certain quasi-hermitian variant of Swanson's model, which is not invariant under conventional $PT$-transformation. The resulting propagator coincides with that of the propagator of the standard harmonic oscillator, which is isospectral with the model under consideration by virtue of a similarity transformation relating the corresponding…
Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry
2015
We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that in both cases, for an appropriate choice of the modulation parameters, the state amplitudes in a generic $n${-}excitation subspace obey the same equations of motion that can be obtained from a \emph{static} non-Hermitian Jaynes-Cummings Hamiltonian with ${\mathcal PT}$ symmetry, that is with an imaginary coupling constant. This gives further support to recent results showing the possible physical interest of ${\mathcal PT}$ symmetric non-Hermitian Hamilto…
Quantum correlations in PT -symmetric systems
2021
Abstract We study the dynamics of correlations in a paradigmatic setup to observe PT -symmetric physics: a pair of coupled oscillators, one subject to a gain one to a loss. Starting from a coherent state, quantum correlations (QCs) are created, despite the system being driven only incoherently, and can survive indefinitely. Both total and QCs exhibit different scalings of their long-time behavior in the PT -broken/unbroken phase and at the exceptional point (EP). In particular, PT symmetry breaking is accompanied by non-zero stationary QCs. This is analytically shown and quantitatively explained in terms of entropy balance. The EP in particular stands out as the most classical configuration…
Pseudo-Bosons from Landau Levels
2010
We construct examples of pseudo-bosons in two dimensions arising from the Hamiltonian for the Landau levels. We also prove a no-go result showing that non-linear combinations of bosonic creation and annihilation operators cannot give rise to pseudo-bosons.
Gibbs states, algebraic dynamics and generalized Riesz systems
2020
In PT-quantum mechanics the generator of the dynamics of a physical system is not necessarily a self-adjoint Hamiltonian. It is now clear that this choice does not prevent to get a unitary time evolution and a real spectrum of the Hamiltonian, even if, most of the times, one is forced to deal with biorthogonal sets rather than with on orthonormal basis of eigenvectors. In this paper we consider some extended versions of the Heisenberg algebraic dynamics and we relate this analysis to some generalized version of Gibbs states and to their related KMS-like conditions. We also discuss some preliminary aspects of the Tomita-Takesaki theory in our context.
A Note on States and Traces from Biorthogonal Sets
2019
In this paper, following Bagarello, Trapani, and myself, we generalize the Gibbs states and their related KMS-like conditions. We have assumed that H 0 , H are closed and, at least, densely defined, without giving information on the domain of these operators. The problem we address in this paper is therefore to find a dense domain D that allows us to generalize the states of Gibbs and take them in their natural environment i.e., defined in L &dagger
Two-qubit entanglement generation through non-Hermitian Hamiltonians induced by repeated measurements on an ancilla
2020
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&ndash