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

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

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

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

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

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

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

Quantum gravitational measure for three-geometries

The gravitational measure on an arbitrary topological three-manifold is constructed. The nontrivial dependence of the measure on the conformal factor is discussed. We show that only in the case of a compact manifold with boundary the measure acquires a nontrivial dependence on the conformal factor which is given by the Liouville action. A nontrivial Jacobian (the divergent part of it) generates the Einstein-Hilbert action. The Hartle-Hawking wave function of Universe is given in terms of the Liouville action. In the gaussian approximation to the Wheeler-DeWitt equation this result was earlier derived by Banks et al. Possible connection with the Chern-Simons gravity is also discussed.Comment: 16 pages, TeX. This is the original, preprint version of the paper that with some modifications was published i

The jet quenching in high energy nuclear collisions and quark-gluon plasma

e investigate the energy loss of quark and gluon jets in quark-gluon plasma produced in central Au+Au collisions at RHIC energy. We use the physical characteristic of initial and mixed phases, which were found in effective quasiparticle model for SPS and RHIC energy. At investigation of energy loss we take into account also the production of hot glue at first stage. The energy loss in expanding plasma is calculated in dominant first order of radiation intensity with accounting of finite kinematic bounds. We calculate the suppression of $\pi^0$ - spectra with moderate high $p_{\perp}$, which is caused by energy loss of quark and gluon jets. The comparison with suppression of $\pi^0$ reported by PHENIX show, that correct quantitative description of suppression we have only in model of phase transition with decrease of thermal gluon mass and effective coupling $G(T)$ in region of phase transition plasma into hadrons (at $T \simeq T_c$). However quasiparticle model with increase of these values at $T \to T_c$ in accordance with perturbative QCD lead to too great energy loss of gluon and quark jets, which disagrees with data on suppression of $\pi^0$. Thus it is possible with help of hard processes to investigate the structure of phase transition. We show also, that energy losses at SPS energy are too small in order to be observable. This is caused in fact by sufficiently short plasma phase at this energy.Comment: 17 pages, 3 figures, 2 table

High order Chin actions in path integral Monte Carlo

High order actions proposed by Chin have been used for the first time in path integral Monte Carlo simulations. Contrarily to the Takahashi-Imada action, which is accurate to fourth order only for the trace, the Chin action is fully fourth order, with the additional advantage that the leading fourth and sixth order error coefficients are finely tunable. By optimizing two free parameters entering in the new action we show that the time step error dependence achieved is best fitted with a sixth order law. The computational effort per bead is increased but the total number of beads is greatly reduced, and the efficiency improvement with respect to the primitive approximation is approximately a factor of ten. The Chin action is tested in a one-dimensional harmonic oscillator, a H$_2$ drop, and bulk liquid $^4$He. In all cases a sixth-order law is obtained with values of the number of beads that compare well with the pair action approximation in the stringent test of superfluid $^4$He.Comment: 19 pages, 8 figure