We construct a finite spin-1/2 chain model (quantum domino) interacting with a Fermi field, capable of emitting a scalar fermion from the last spin in the chain. The chain with dynamics gradually reversing the neighbouring spins emits eventually a fermion which escapes then to infinity, and the chain converges to a stationary state. We determine the rate of convergence of the system for large time to a different "macroscopic" state connected with the emission of a fermion. We prove that the probability of fermion emission as a function of time t approaches to unity "almost exponentially". We propose that this fast rate of convergence could serve as an approximate theoretical possibility for the "effective" description of the quantum measurement process in the sense proposed by K. Hepp. This all will be preceded by an outline of explicitly solvable dynamics of infinite version of the spin chain which exhibits transition from a locally perturbed unstable stationary state to a truly macroscopically different (i.e. disjoint) state, but with slow convergence for t approaching to infinity.We construct a finite spin-1/2 chain model (quantum domino) interacting with a Fermi field, capable of emitting a scalar fermion from the last spin in the chain. The chain with dynamics gradually reversing the neighbouring spins emits eventually a fermion which escapes then to infinity, and the chain converges to a stationary state. We determine the rate of convergence of the system for large time to a different "macroscopic" state connected with the emission of a fermion. We prove that the probability of fermion emission as a function of time t approaches to unity "almost exponentially". We propose that this fast rate of convergence could serve as an approximate theoretical possibility for the "effective" description of the quantum measurement process in the sense proposed by K. Hepp. This all will be preceded by an outline of explicitly solvable dynamics of infinite version of the spin chain which exhibits transition from a locally perturbed unstable stationary state to a truly macroscopically different (i.e. disjoint) state, but with slow convergence for t approaching to infinity.

arXiv:1211.6783Nov 28, 20120 citations

Correlation dynamics of finite fermion systems

W. Cassing, A. Pfitzner

The European Physical Journal AJun 1, 19904 citations

Integrability of Fermionic Dynamics

WORLD SCIENTIFIC eBooksMar 1, 20010 citations

Quantum control of infinite-dimensional many-body systems

Roger S. Bliss, Daniel Klaus Burgarth

A major challenge to the control of infinite-dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space domain and show that by utilizing the implications of the quantum recurrence theorem this irreversibility may be overcome, in the case of individual states more generally, but also in certain specified cases over larger subsets of the Hilbert space. We discuss briefly the possibility of using these results in the control of infinite-dimensional coupled harmonic oscillators and also draw attention to some of the issues and open questions arising from this and related work.A major challenge to the control of infinite-dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space domain and show that by utilizing the implications of the quantum recurrence theorem this irreversibility may be overcome, in the case of individual states more generally, but also in certain specified cases over larger subsets of the Hilbert space. We discuss briefly the possibility of using these results in the control of infinite-dimensional coupled harmonic oscillators and also draw attention to some of the issues and open questions arising from this and related work.

arXiv:1308.4629Physical Review AMar 10, 201410 citations

Time irreversibility in the quantum systems with infinite number of particles

Huo Yuping

The time irreversible evolution of quantum systems with infinite number of particles (QSINP) was studied within a newly constructed algebraic framework. The QSINP could be described by the quantum infinite lattice field. The *-Algebra R is the set of all dynamic variables of the QSINP, in which a special addition and multiplication operations were defined. The full pure state vector (FPSV) ρ, the pure state vector {ρ_f} and the equivalent relations within them are also well defined. The set of all pure state vectors, which are equivalent to the FPSV ρ, is a Hilbert Space {H_ρ}, if the addition, the inner product and the norm were defined in it. The set of all linear transformation {N_ρ} on {H_ρ} is isomorphic to R, and {{N_ρ},{H_ρ}} is the representation of R, associated with ρ. The *-Algebra R has infinitely many non-equivalent irreducible GNS constructions (representations), associated with different nonequivalent FPSVs respectively. It is proved that, the dynamical motions of the QSINP is totally within the GNS construction associated with the initial pure state vector; However, the time reversal transformation makes the initial FPSV and its corresponding dynamical evolution into another non-equivalent GNS construction. Therefore, within the GNS construction associated with the FPSV, the dynamics of the QSINP is time irreversible. Finally, due to the Liouville operator has real continuous spectrum within the GNS construction, the longtime asymptotic solution of Liouville equation in the GNS construction could be treated by the formal scattering theory. The Master equation with dissipative term was obtained, which is formally irrelevant of the initial state and the corresponding GNS construction. This master equation could be regarded as the evolution equation of the QSINP on R.The time irreversible evolution of quantum systems with infinite number of particles (QSINP) was studied within a newly constructed algebraic framework. The QSINP could be described by the quantum infinite lattice field. The *-Algebra R is the set of all dynamic variables of the QSINP, in which a special addition and multiplication operations were defined. The full pure state vector (FPSV) ρ, the pure state vector {ρ_f} and the equivalent relations within them are also well defined. The set of all pure state vectors, which are equivalent to the FPSV ρ, is a Hilbert Space {H_ρ}, if the addition, the inner product and the norm were defined in it. The set of all linear transformation {N_ρ} on {H_ρ} is isomorphic to R, and {{N_ρ},{H_ρ}} is the representation of R, associated with ρ. The *-Algebra R has infinitely many non-equivalent irreducible GNS constructions (representations), associated with different nonequivalent FPSVs respectively. It is proved that, the dynamical motions of the QSINP is totally within the GNS construction associated with the initial pure state vector; However, the time reversal transformation makes the initial FPSV and its corresponding dynamical evolution into another non-equivalent GNS construction. Therefore, within the GNS construction associated with the FPSV, the dynamics of the QSINP is time irreversible. Finally, due to the Liouville operator has real continuous spectrum within the GNS construction, the longtime asymptotic solution of Liouville equation in the GNS construction could be treated by the formal scattering theory. The Master equation with dissipative term was obtained, which is formally irrelevant of the initial state and the corresponding GNS construction. This master equation could be regarded as the evolution equation of the QSINP on R.

arXiv:1312.7741Dec 24, 20130 citations

Lieb-Robinson bounds for irreversible dynamics via adaptive Dyson expansion

Carla Rubiliani, Marius Wesle, Tom Wessel

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

[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.