It is shown, that quantum theory with complex evolutionary time parameter and non-Hermitian Hamiltonian structure can be used for natural unification of quantum and thermodynamic principles. The theory is postulated as analytical in respect to the parameter of evolution, which real part is identified with the `usual' physical time, whereas the imaginary one is understood as proportional to the inverse absolute temperature. Also, the Hermitian part of the Hamiltonian is put equal to conventional operator of energy. It is shown, that the anti-Hermitian Hamiltonian part, which is taken as commuting with the energy operator, is constructed from parameters of decay of the system. It is established, that quantum dynamics, predicted by this theory, is integrable in the same sense as the corresponding non-modified one, and that it possesses a well defined arrow of time in isothermal and adiabatic regimes of the evolution. It is proved, that average value of the decay operator decreases monotonously (as the function of the physical time) in these important thermodynamical regimes for the arbitrary initial data taken. We discuss possible application of the general formalism developed to construction of time-irreversible modification of a string theory.It is shown, that quantum theory with complex evolutionary time parameter and non-Hermitian Hamiltonian structure can be used for natural unification of quantum and thermodynamic principles. The theory is postulated as analytical in respect to the parameter of evolution, which real part is identified with the `usual' physical time, whereas the imaginary one is understood as proportional to the inverse absolute temperature. Also, the Hermitian part of the Hamiltonian is put equal to conventional operator of energy. It is shown, that the anti-Hermitian Hamiltonian part, which is taken as commuting with the energy operator, is constructed from parameters of decay of the system. It is established, that quantum dynamics, predicted by this theory, is integrable in the same sense as the corresponding non-modified one, and that it possesses a well defined arrow of time in isothermal and adiabatic regimes of the evolution. It is proved, that average value of the decay operator decreases monotonously (as the function of the physical time) in these important thermodynamical regimes for the arbitrary initial data taken. We discuss possible application of the general formalism developed to construction of time-irreversible modification of a string theory.

arXiv:hep-th/0612122Dec 13, 20064 citations

Decay of Correlations for Quantum Spin Systems with a Transverse Field: A Dynamic Approach

Alessandra Cipriani, Paolo Dai Pra

We consider a wide class of quantum spin systems obtained by adding a transverse field to a classical Hamiltonian. We give explicit high-temperature conditions which guarantee exponential decay of correlations. A stochastic-geometric representation allows to reformulate the model as a classical random field on a space of marked point processes on the circle $[0,β)$ , where $β$ is the inverse temperature. We then construct a Markov process having this random field as invariant measure. By the mixing properties of the process, the exponential decay of correlations follows by an adaptation of a general argument.We consider a wide class of quantum spin systems obtained by adding a transverse field to a classical Hamiltonian. We give explicit high-temperature conditions which guarantee exponential decay of correlations. A stochastic-geometric representation allows to reformulate the model as a classical random field on a space of marked point processes on the circle $[0,β)$, where $β$ is the inverse temperature. We then construct a Markov process having this random field as invariant measure. By the mixing properties of the process, the exponential decay of correlations follows by an adaptation of a general argument.

arXiv:1005.3547May 19, 20103 citations

Quantum Dynamics: From Automorphism to Hamiltonian

Barry Simon A

Princeton University Press eBooksApr 24, 201518 citations

Dynamics of Quantum Systems with Interacting Particles

Elisheva Elbaz

Apr 1, 20160 citations

Explicit construction of local conserved operators in disordered many-body systems

Thomas E. O’Brien, Dmitry A. Abanin, Guifré Vidal +1 more

The presence and character of local integrals of motion---quasilocal operators that commute with the Hamiltonian---encode valuable information about the dynamics of a quantum system. In particular, strongly disordered many-body systems can generically avoid thermalization when there are extensively many such operators. In this work, we explicitly construct local conserved operators in one-dimensional spin chains by directly minimizing their commutator with the Hamiltonian. We demonstrate the existence of an extensively large set of local integrals of motion in the many-body localized phase of the disordered XXZ spin chain. These operators are shown to have exponentially decaying tails, in contrast to the ergodic phase where the decay is (at best) polynomial in the size of the subsystem. We study the algebraic properties of localized operators and confirm that in the many-body localized phase, they are well described by ``dressed'' spin operators.The presence and character of local integrals of motion---quasilocal operators that commute with the Hamiltonian---encode valuable information about the dynamics of a quantum system. In particular, strongly disordered many-body systems can generically avoid thermalization when there are extensively many such operators. In this work, we explicitly construct local conserved operators in one-dimensional spin chains by directly minimizing their commutator with the Hamiltonian. We demonstrate the existence of an extensively large set of local integrals of motion in the many-body localized phase of the disordered XXZ spin chain. These operators are shown to have exponentially decaying tails, in contrast to the ergodic phase where the decay is (at best) polynomial in the size of the subsystem. We study the algebraic properties of localized operators and confirm that in the many-body localized phase, they are well described by ``dressed'' spin operators.

arXiv:1608.03296Physical review. B./Physical review. BOct 24, 201658 citations

[0,β)

, where

β

is the inverse temperature. We then construct a Markov process having this random field as invariant measure. By the mixing properties of the process, the exponential decay of correlations follows by an adaptation of a general argument.