Avoiding irreversible dynamics in quantum systems

In this note, we study a broad class of time-dependent and irreversible dynamics for quantum spin systems in both finite and infinite volume. We develop a simple and flexible strategy for expanding commutators of the form $[A,τ_{s,t} \, B]$ in terms of self-avoiding paths of sets, where $A$ and $B$ are local operators and $τ_{s,t}$ is the Heisenberg time evolution. This adaptive Dyson expansion requires no backwards time evolution and is thus also applicable to irreversible dynamics. Furthermore, we discuss how such an expansion directly implies Lieb-Robinson bounds. A central feature of our result is that the obtained Lieb-Robinson bounds are independent of any Hamiltonian and dissipative on-site terms of the generator.In this note, we study a broad class of time-dependent and irreversible dynamics for quantum spin systems in both finite and infinite volume. We develop a simple and flexible strategy for expanding commutators of the form $[A,τ_{s,t} \, B]$ in terms of self-avoiding paths of sets, where $A$ and $B$ are local operators and $τ_{s,t}$ is the Heisenberg time evolution. This adaptive Dyson expansion requires no backwards time evolution and is thus also applicable to irreversible dynamics. Furthermore, we discuss how such an expansion directly implies Lieb-Robinson bounds. A central feature of our result is that the obtained Lieb-Robinson bounds are independent of any Hamiltonian and dissipative on-site terms of the generator.

math-phCross-listedarXiv:2610.12731Oct 12, 20260 citations

Irreversible Quantum Dynamics

Fabio Benatti, Roberto Floreanini B

Lecture notes in physicsJan 1, 2003327 citations

Irreversibility and chaos in quantum systems

Giulio Casati

Lecture notes in mathematicsJan 1, 19842 citations

Dynamical stabilization and time in open quantum systems

I. Rotter

The meaning of time in an open quantum system is considered under the assumption that both, system and environment, are quantum mechanical objects. The Hamilton operator of the system is non-Hermitian. Its imaginary part is the time operator. As a rule, time and energy vary continuously when controlled by a parameter. At high level density, where many states avoid crossing, a dynamical phase transition takes place in the system under the influence of the environment. It causes a dynamical stabilization of the system what can be seen in many different experimental data. Due to this effect, time is bounded from below: the decay widths (inverse proportional to the lifetimes of the states) do not increase limitless. The dynamical stabilization is an irreversible process.The meaning of time in an open quantum system is considered under the assumption that both, system and environment, are quantum mechanical objects. The Hamilton operator of the system is non-Hermitian. Its imaginary part is the time operator. As a rule, time and energy vary continuously when controlled by a parameter. At high level density, where many states avoid crossing, a dynamical phase transition takes place in the system under the influence of the environment. It causes a dynamical stabilization of the system what can be seen in many different experimental data. Due to this effect, time is bounded from below: the decay widths (inverse proportional to the lifetimes of the states) do not increase limitless. The dynamical stabilization is an irreversible process.

Feb 1, 201310 citations

Dynamical stabilization and time in open quantum systems

I. Rotter

Abstract The meaning of time in an open quantum system is considered under the assumption that both, system and environment, are quantum mechanical objects. The Hamilton operator of the system is non‐Hermitian. Its imaginary part is the time operator. As a rule, time and energy vary continuously when controlled by a parameter. At high level density, where many states avoid crossing, a dynamical phase transition takes place in the system under the influence of the environment. It causes a dynamical stabilization of the system what can be seen in many different experimental data. Due to this effect, time is bounded from below: the decay widths (inverse proportional to the lifetimes of the states) do not increase limitless. The dynamical stabilization is an irreversible process.Abstract The meaning of time in an open quantum system is considered under the assumption that both, system and environment, are quantum mechanical objects. The Hamilton operator of the system is non‐Hermitian. Its imaginary part is the time operator. As a rule, time and energy vary continuously when controlled by a parameter. At high level density, where many states avoid crossing, a dynamical phase transition takes place in the system under the influence of the environment. It causes a dynamical stabilization of the system what can be seen in many different experimental data. Due to this effect, time is bounded from below: the decay widths (inverse proportional to the lifetimes of the states) do not increase limitless. The dynamical stabilization is an irreversible process.

arXiv:1206.1813Fortschritte der PhysikJun 18, 201217 citations

[A,τ_{s,t} \, B]

in terms of self-avoiding paths of sets, where

A

and

B

are local operators and

τ_{s,t}

is the Heisenberg time evolution. This adaptive Dyson expansion requires no backwards time evolution and is thus also applicable to irreversible dynamics. Furthermore, we discuss how such an expansion directly implies Lieb-Robinson bounds. A central feature of our result is that the obtained Lieb-Robinson bounds are independent of any Hamiltonian and dissipative on-site terms of the generator.