Related papers: On the General Form of Quantum Stochastic Evolutio…
In a companion paper we derived a unique time-reversal-invariant stochastic generalization of the Liouville equation and showed that it coincides with the evolution equation for the Husimi $Q$-function in a broad class of bosonic quantum…
The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic…
The quantum regression formula for an open quantum system consists in an infinite hierarchy of conditions for its multi-time correlation functions, thus requiring full access to the total "system+environment" evolution, and providing a…
We use a noncommutative generalization of Fourier analysis to define a broad class of pseudo-probability representations, which includes the known bosonic and discrete Wigner functions. We characterize the groups of quantum unitary…
Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the…
Quantum dynamical time-evolution of bosonic fields is shown to be equivalent to a stochastic trajectory in space-time, corresponding to samples of a statistical mechanical steady-state in a higher dimensional quasi-time. This is proved…
We consider the problem of an electron tunneling between two coupled quantum dots, a two-state quantum system (qubit), using a low-transparency point contact (PC) or tunnel junction as a detector continually measuring the position of the…
An equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics. The equation is solved by using the singular perturbation method, and assuming that the number of bases in the…
Quantum dynamics of the density operator in the framework of a single probability vector is analyzed. In this framework quantum states define a proper convex quantum subset in an appropriate simplex. It is showed that the corresponding…
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…
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…
Hierarchical decays of $N$ matter species to radiation may balance against Hubble expansion to yield stasis, a new phase of cosmological evolution with constant matter and radiation abundances. We analyze stasis with various machine…
The Loewner equation, in its stochastic incarnation introduced by Schramm, is an insightful method for the description of critical random curves and interfaces in two-dimensional statistical mechanics. Two features are crucial, namely…
We develop a consistent perturbation theory in quantum fluctuations around the classical evolution of a system of interacting bosons. The zero order approximation gives the classical Gross-Pitaevskii equations. In the next order we recover…
We consider the problem of understanding the basic features displayed by quantum systems described by parametric oscillators whose time-dependent frequency parameter $\omega(t)$ varies continuously during evolution so to realise quenching…
The coherent quantum evolution of a one-dimensional many-particle system after sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and non-integrable regimes. It is…
We define a generalized rate equation for an observable in quantum mechanics, that involves a parameter q and whose limit $q\to 1$ gives the standard Heisenberg equation. The generalized rate equation is used to study dynamics of current…
We review the Lee-Friedrichs model as a model of atomic resonances in the hydrogen atom, using the dipole-moment matrix-element functions which have been exactly computed by Nussenzveig. The Hamiltonian $H$ of the model is positive and has…
A generalized definition of quantum stochastic (QS) integrals and differentials is given in the free of adaptiveness and dimensionality form in terms of Malliavin derivative on a projective Fock space, and their uniform continuity with…
A non-local toy-model is proposed for the purpose of modelling the ``wave function collapse'' of a two-state quantum system. The collapse is driven by a nonlinear evolution equation with an extreme sensitivity to absolute phase. It is…