Related papers: Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries

Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries

URL: http://arxiv.org/abs/2304.02367v2
Date: Thu, 3 Aug 2023 12:07:14 GMT
Title: Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries
Authors: Steven Kim and Fabian Hassler
Abstract summary: We show that the non-Hermitian effective Hamiltonian of the system, next to incorporating the dynamics of the system, is a tool to analyze its symmetries. As an example, we use the effective Hamiltonian to formulate a $mathcalPT$-symmetry' of an open system.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Open quantum systems that interact with a Markovian environment can be described by a Lindblad master equation. The generator of time-translation is given by a Liouvillian superoperator $\mathcal{L}$ acting on the density matrix of the system. As the Fock space for a single bosonic mode is already infinite-dimensional, the diagonalization of the Liouvillian has to be done on the creation- and annihilation-superoperators, a process called `third quantization'. We propose a method to solve the Liouvillian for quadratic systems using a single symplectic transformation. We show that the non-Hermitian effective Hamiltonian of the system, next to incorporating the dynamics of the system, is a tool to analyze its symmetries. As an example, we use the effective Hamiltonian to formulate a $\mathcal{PT}$-`symmetry' of an open system. We describe how the inclusion of source terms allows us to obtain the cumulant generating function for observables such as the photon current.

Related papers

Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
arXiv Detail & Related papers (2023-02-27T18:56:40Z)
Quantum generalized Calogero-Moser systems from free Hamiltonian reduction [0.0]
The one-dimensional system of particles with a $1/x2$ repulsive potential is known as the Calogero-Moser system. We present a detailed and rigorous derivation of the generalized quantum Calogero-Moser Hamiltonian.
arXiv Detail & Related papers (2022-11-10T18:34:17Z)
Bootstrapping the gap in quantum spin systems [0.7106986689736826]
We use the equations of motion to develop an analogue of the conformal block expansion for matrix elements. The method can be applied to any quantum mechanical system with a local Hamiltonian.
arXiv Detail & Related papers (2022-11-07T19:07:29Z)
The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
arXiv Detail & Related papers (2022-04-16T07:03:54Z)
Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems [2.0305676256390934]
The dynamics of Markovian open quantum systems are described by Lindblad master equations. We show how the Liouvillian can be transformed to a many-body Jordan normal form. Results on criticality and dissipative phase transitions are discussed in a companion paper.
arXiv Detail & Related papers (2021-12-15T18:52:58Z)
Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
arXiv Detail & Related papers (2021-09-27T17:45:42Z)
Non-Hermitian quantum walks and non-Markovianity: the coin-position interaction [2.501693072047969]
We compare the two methods of constructing the reduced dynamics of a system evolving under a non-Hermitian Hamiltonian. We find that under the metric formalism, a power law decay of the information backflow to the subsystem gives a clear indication of the transition from $mathcalPT$-unbroken to the broken phase.
arXiv Detail & Related papers (2021-09-22T12:21:36Z)
Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
arXiv Detail & Related papers (2021-02-18T20:55:04Z)
Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
arXiv Detail & Related papers (2021-02-02T13:56:11Z)
Dissipative flow equations [62.997667081978825]
We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode.
arXiv Detail & Related papers (2020-07-23T14:47:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.