Two interacting spins in external fields. Four-level systems

In the present article, we consider the so-called two-spin equation that describes four-level quantum systems. Recently, these systems attract attention due to their relation to the problem of quantum computation. We study general properties of the two-spin equation and show that the problem for certain external backgrounds can be identified with the problem of one spin in an appropriate background. This allows one to generate a number of exact solutions for two-spin equations on the basis of already known exact solutions of the one-spin equation. Besides, we present some exact solutions for the two-spin equation with an external background different for each spin but having the same direction. We study the eigenvalue problem for a time-independent spin interaction and a time-independent external background. A possible analogue of the Rabi problem for the two-spin equation is defined. We present its exact solution and demonstrate the existence of magnetic resonances in two specific frequencies, one of them coinciding with the Rabi frequency, and the other depending on the rotating field magnitude. The resonance that corresponds to the second frequency is suppressed with respect to the first one.Comment: 14 page

Wigner distribution functions for complex dynamical systems: a path integral approach

Starting from Feynman's Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the classical phase space trajectory is found to contribute to the propagator. Inspired by Feynman's and Vernon's influence functional theory we extend the method to calculate the propagator for the reduced Wigner function of a system of interest coupled to an external system. Explicit expressions are obtained when the external system consists of a set of independent harmonic oscillators. As an example we calculate the propagator for the reduced Wigner function associated with the Caldeira-Legett model

Spin equation and its solutions

The aim of the present article is to study in detail the so-called spin equation (SE) and present both the methods of generating new solution and a new set of exact solutions. We recall that the SE with a real external field can be treated as a reduction of the Pauli equation to the (0+1)-dimensional case. Two-level systems can be described by an SE with a particular form of the external field. In this article, we also consider associated equations that are equivalent or (in one way or another) related to the SE. We describe the general solution of the SE and solve the inverse problem for this equation. We construct the evolution operator for the SE and consider methods of generating new sets of exact solutions. Finally, we find a new set of exact solutions of the SE.Comment: 29 page

Generalized Aharonov-Bohm effect, homotopy classes and Hausdorff dimension

We suggest as gedanken experiment a generalization of the Aharonov-Bohm experiment, based on an array of solenoids. This experiment allows in principle to measure the decomposition into homotopy classes of the quantum mechanical propagator. This yields information on the geometry of the average path of propagation and allows to determine its Hausdorff dimension.Comment: 14 pages, LaTeX + 3 figures, P

Geometrical Phase Transitions

The geometrical approach to phase transitions is illustrated by simulating the high-temperature representation of the Ising model on a square lattice.Comment: 5 pages, 3 figures, talk presented at Conference on Computational Physics 2004, Genoa, 1-4 September 2004; 2nd version: slightly expanded versio

J-factors of short DNA molecules

The propensity of short DNA sequences to convert to the circular form is studied by a mesoscopic Hamiltonian method which incorporates both the bending of the molecule axis and the intrinsic twist of the DNA strands. The base pair fluctuations with respect to the helix diameter are treated as path trajectories in the imaginary time path integral formalism. The partition function for the sub-ensemble of closed molecules is computed by imposing chain ends boundary conditions both on the radial fluctuations and on the angular degrees of freedom. The cyclization probability, the J-factor, proves to be highly sensitive to the stacking potential, mostly to its nonlinear parameters. We find that the J-factor generally decreases by reducing the sequence length ( N ) and, more significantly, below N = 100 base pairs. However, even for very small molecules, the J-factors remain sizeable in line with recent experimental indications. Large bending angles between adjacent base pairs and anharmonic stacking appear as the causes of the helix flexibility at short length scales.Comment: The Journal of Chemical Physics - May 2016 ; 9 page

Interplanetary Particle Environment. Proceedings of a Conference

A workshop entitled the Interplanetary Charged Particle Environment was held at the Jet Propulsion Laboratory (JPL) on March 16 and 17, 1987. The purpose of the Workshop was to define the environment that will be seen by spacecraft operating in the 1990s. It focused on those particles that are involved in single event upset, latch-up, total dose and displacement damage in spacecraft microelectronic parts. Several problems specific to Magellan were also discussed because of the sensitivity of some electronic parts to single-event phenomena. Scientists and engineers representing over a dozen institutions took part in the meeting. The workshop consisted of two major activities, reviews of the current state of knowledge and the formation of working groups and the drafting of their reports

Quantum initial condition sampling for linearized density matrix dynamics: Vibrational pure dephasing of iodine in krypton matrices

This paper reviews the linearized path integral approach for computing time dependent properties of systems that can be approximated using a mixed quantum-classical description. This approach is applied to studying vibrational pure dephasing of ground state molecular iodine in a rare gas matrix. The Feynman-Kleinert optimized harmonic approximation for the full system density operator is used to sample initial conditions for the bath degrees of freedom. This extremely efficient approach is compared with alternative initial condition sampling techniques at low temperatures where classical initial condition sampling yields dephasing rates that are nearly an order of magnitude too slow compared with quantum initial condition sampling and experimental results.Comment: 20 pages and 8 figure

Bose Fluids Above Tc: Incompressible Vortex Fluids and "Supersolidity"

This paper emphasizes that non-linear rotational or diamagnetic susceptibility is characteristic of Bose fluids above their superfluid Tcs, and for sufficiently slow rotation or weak B-fields amounts to an incompressible response to vorticity. The cause is a missing term in the conventionally accepted model Hamiltonian for quantized vortices in the Bose fluid. The resulting susceptibility can account for recent observations of Chan et al on solid He, and Ong et al on cuprate superconductors

Linear quantum state diffusion for non-Markovian open quantum systems

We demonstrate the relevance of complex Gaussian stochastic processes to the stochastic state vector description of non-Markovian open quantum systems. These processes express the general Feynman-Vernon path integral propagator for open quantum systems as the classical ensemble average over stochastic pure state propagators in a natural way. They are the coloured generalization of complex Wiener processes in quantum state diffusion stochastic Schrodinger equations.Comment: 9 pages, RevTeX, appears in Physics Letters