Related papers: Numerical analysis of a spontaneous collapse model…
Recently, open systems with balanced, spatially separated loss and gain have been realized and studied using non-Hermitian Hamiltonians that are invariant under the combined parity and time-reversal ($\mathcal{PT}$) operations. Here, we…
Here we present a non-Hermitian framework for modeling state-vector collapse under unified dynamics described by Schr\"odinger's equation. Under the premise of non-Hermitian Hamiltonian dynamics, we argue that collapse has to occur when the…
We revisit the concepts of spin relaxation and spin decoherence of two level (spin-1/2) systems. From two toy-models, we clarify two issues related to the spin relaxation and decoherence: 1) For an ensemble of two-level particles each…
The effect of multiplicative stochastic perturbations on Hamiltonian systems on the plane is investigated. It is assumed that perturbations fade with time and preserve a stable equilibrium of the limiting system. The paper investigates…
We analyze the non-Markovian stochastic Schroedinger equation describing a particle subject to spontaneous collapses in space (in the language of collapse models), or subject to a continuous measurement of its position (in the language of…
Chains of first-order SUSY transformations for the spin equation are studied in detail. It is shown that the transformation chains are related with a olynomial pseudo-supersymmetry of the system. Simple determinant formulas for the final…
We study systematically the non-Markovian decoherence dynamics of a dissipative two-level system, i.e., the so-called spin-boson model. It is interesting to find that the decoherence tends to be inhibited with the increase of the coupling…
Slowing down phenomena occur in both deterministic and stochastic dynamical systems at the vicinity of phase transitions or bifurcations. An example is found in systems exhibiting a saddle-node bifurcation, which undergo a dramatic time…
We investigate cosmological models described by a scalar field with an exponential potential, and apply the stochastic formalism, which allows us to study how quantum field fluctuations give rise to stochastic noise. This modifies the…
We discuss a model of spontaneous collapse of the quantum state that does not require adding any stochastic processes to the standard dynamics. The additional ingredient with respect to the wave function is a position in the configuration…
For chaotic systems there is a theory for the decay of the survival probability, and for the parametric dependence of the local density of states. This theory leads to the distinction between "perturbative" and "non-perturbative" regimes,…
We examine two exactly solvable models of decoherence -- a central spin-system, (i) with and (ii) without a self--Hamiltonian, interacting with a collection of environment spins. In the absence of a self--Hamiltonian we show that in this…
This paper concerns the small-time stabilization of some classes of mechanical systems which are not stabilizable by means of at least continuous state feedback laws. This is the case of nonholonomic mechanical systems, an example being the…
We calculate the geometric phase for different open systems (spin-boson and spin-spin models). We study not only how they are corrected by the presence of the different type of environments but also discuss the appearence of decoherence…
Spontaneous collapse models use non-linear stochastic modifications of the Schroedinger equation to suppress superpositions of eigenstates of the measured observable and drive the state to an eigenstate. It was recently demonstrated that…
Analytical tools are extremely hard to find for non-linear gravitational collpase. Only a few simple but powerful tools exist so far. Two examples are the spherical collapse model (SCM) and stable clustering hypothesis (SCH). We present a…
We solve equations, describing in a simplified way the newtonian dynamics of a selfgravitating nonrotating spheroidal body after loss of stability. We find that contraction to a singularity happens only in a pure spherical collapse, and…
We consider fully many-body localized systems, i.e. isolated quantum systems where all the many-body eigenstates of the Hamiltonian are localized. We define a sense in which such systems are integrable, with localized conserved operators.…
The notion of collapse is discussed and refined within the Two-State-Vector Formalism (TSVF). We show how a definite result of a measurement can be fully determined when considering specific forward and backward-evolving quantum states.…
Muon spin relaxation is a powerful technique for probing static and dynamic local magnetic fields. The strong collision model, based on a Gaussian-Markovian process, is commonly used to account for dynamical effects. Yet, it remains limited…