Related papers: Transition Probability for Class of Two Level Syst…
The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two…
The maximum likelihood state for a simplified stochastic thermohaline circulation model is investigated. It is shown that a jump occurs for the maximum likelihood state during transitions between two metastable states. The jump helps to…
We determine the propagation properties of a quantum particle in a d-dimensional lattice with hopping disorder, delta-correlated in time. The system is delocalized: the averaged transition probability shows a diffusive behavior. Then,…
In this work, we derive exact solutions of a dynamical equation, which can represent all two-level Hermitian systems driven by periodic $N$-step driving fields. For different physical parameters, this dynamical equation displays various…
The escape rate \Gamma of the large-spin model described by the Hamiltonian H = -DS_z^2 - H_zS_z - H_xS_x is investigated with the help of the mapping onto a particle moving in a double-well potential U(x). The transition-state method…
Couplings of a system to other degrees of freedom (that is, environmental degrees of freedom) lead to energy dissipation when the number of environmental degrees of freedom is large enough. Here we discuss quantal treatments for such energy…
We study the transition time distribution for a particle moving between two wells of a multidimensional potential in the low-noise limit of overdamped Langevin dynamics. Possible transition paths are restricted to a thin tube surrounding…
The time-dependent behavior of a two-level system interacting with a quantum oscillator system is analyzed in the case of a coupling larger than both the energy separation between the two levels and the energy of quantum oscillator ($\Omega…
In this paper we prove two extensions of Hamilton's maximal principle for systems pf parabolic equations which sould be useful for the study of the Ricci flow and some other geometric evolution equations. One extension is a time-dependent…
We show that a proportionality between the entanglement Hamiltonian and the Hamiltonian of a subsystem exists near the limit of maximal entanglement under certain conditions. Away from that limit, solvable models show that the coupling…
We consider real analytic Hamiltonians whose flow depends linearly on time. Trivial examples are Hamiltonians $H(q,p)$ that do not depend on the coordinate $q$. By a theorem of Moser, every polynomial Hamiltonian of degree 3 reduces to such…
We consider a time dependent trap externally manipulated in such a way that one of its bound states is brought up towards the continuum threshold, and then down again. We evaluate the probability $P^{stay}$ for a particle, initially in a…
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,…
For autonomous systems it is well known how to extract tunneling probabilities from wavepacket calculations. Here we present a corresponding approach for periodically time-dependent Hamiltonians, valid at all frequencies, field strengths,…
The escape rates of the biaxial single domain spin particles with and without an applied magnetic field are investigated. Using the strict potential field description of spin systems developed by Ulyanov and Zaslavskii we obtain new…
Testable conditional probabilities appear to be restricted to single hypersurfaces (marvelous moments) and depend only on stationary observables. Observable evolution, such as a change of entropy, should be expressed as a dependence upon…
We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey class $G^\alpha$ as a function of time, and we show that the…
We establish stability criterion for a two-class retrial system with Poisson inputs, general class-dependent service times and class-dependent constant retrial rates. We also characterise an interesting phenomenon of partial stability when…
Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single valued integrals of motion each. All…
Hamiltonian systems with linearly dependent constraints (irregular systems), are classified according to their behavior in the vicinity of the constraint surface. For these systems, the standard Dirac procedure is not directly applicable.…