Radical anions of trimethyl and triphenyl lead chloride and of triphenyl lead bromide: an E.S.R. study

We report the gas phase microwave observation and subsequent analysis of the ring puckering level splitting of indoline and its N-D isotopomer. The spectra of the four lowest vibrational states are modelled through a two-dimensional vibrational Hamiltonian to furnish a coherent picture. According to this new picture, five-membered rings with a single double bond and five-membered rings in which the double bond is fused with a benzenic ring share a similar low ring puckering barrier. Discrepancies with previous work are ascribed to the use of a one-dimensional vibrational Hamiltonian. Ab initio calculations concur with the present analysis.     

THEORY OF THE P=2 LOCK-IN PHASE TRANSITION IN SURFACE RECONSTRUCTION

The p=2 lock-in phase transition in surface reconstruction is studied within the soliton picture by a two-dimensional lattice effective Hamiltonian,which has the coupling of the semiinfinite crystal.An analytical form of the p=2 soliton is obtained.Having complicated structure and narrowed width,the Soliton solution is found to be different from the ordinary form.This behavior is due to the coupled extra dis-tortion of the incommensurate phase in the surface reconstruction,and is necessary for the p=2 lock-in phase transition.The theory is consistent with many known experimental results and is applicable to other physical systems.     

An underlying geometrical manifold for Hamiltonian mechanics

We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture), that can be put into correspondence with the usual Hamilton–Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamiltonian–Lagrange picture, defined on the Hamilton–Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton–Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton–Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the the original Hamiltonian motion.     

Continuous phase transition in a spin-glass model without time-reversal symmetry

We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time-reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however, in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific-heat exponent. We expect the nature of the transition in this three-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.     

Two-electron quantum dot molecule: composite particles and the spin phase diagram

We study a two-electron quantum dot molecule in a magnetic field by the direct diagonalization of the Hamiltonian matrix. The ground states of the molecule with the total spin S = 0 and S = 1 provide a possible realization for a qubit of a quantum computer. Switching between the states is best achieved by changing the magnetic field. Based on an analysis of the wave function, we show that the system consists of composite particles formed by an electron and flux quanta attached to it. This picture can also be used to explain the spin phase diagram.     

Hard-core bosonization of the one-dimensional t-J model

The one-dimensional t-J model Hamiltonian is realized by using hard-core boson operators. A simple algorithm written in Mathematica based on a differential realization of the hard-core bosons for finding exact solutions of the model is proposed. As a simple example, some low-lying excitation energies, the inverse compressibility, and the superconducting structure factors, as well as the particle and spin entanglement of a system with 8 sites are calculated. The results not only confirm the validity of the hard-core boson picture, but also indicate that a quantum phase transition near phase-separation at zero temperature can also be recognized by the particle and spin entanglement.     

First-Order Phase Transitions in One-Dimensional Steady States

The steady states of the two-species (positive and negative particles) asymmetric exclusion model of Evans, Foster, Godrèche, and Mukamel are studied using Monte Carlo simulations. We show that mean-field theory does not give the correct phase diagram. On the first-order phase transition line which separates the CP-symmetric phase from the broken phase, the density profiles can be understood through an unexpected pattern of shocks. In the broken phase the free energy functional is not a convex function, but looks like a standard Ginzburg–Landau picture. If a symmetry-breaking term is introduced in the boundaries, the Ginzburg–Landau picture remains and one obtains spinodal points. The spectrum of the Hamiltonian associated with the master equation was studied using numerical diagonalization. There are massless excitations on the first-order phase transition fine with a dynamical critical exponent z = 2, as expected from the existence of shocks, and at the spinodal points, where we find z = 1. It is the first time that this value, which characterizes conformal invariant equilibrium problems, appears in stochastic processes.     

Quantum treatment of the time-dependent coupled oscillators under the action of a random force

In this communication we introduce the problem of time-dependent frequency converter under the action of external random force. We have assumed that the coupling parameter and the phase pump are explicitly time dependent. Using the equations of motion in the Heisenberg picture the dynamical operators are obtained, however, under a certain integrability condition. When the system is initially prepared in the even coherent states the squeezing phenomenon is discussed. The correlation function is also considered and it has been shown that the nonclassical properties are apparent and sensitive to any variation in the integrability parameter. Furthermore, the wave function in Schrödinger picture is calculated and used it to derive the wave function in the coherent states. The accurate definition of the creation and annihilation operators are also introduced and employed to diagonalize the Hamiltonian system.     

Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians

For a large class of time-dependent non-Hermitian Hamiltonians expressed in terms linear and bilinear combinations of the generators for an Euclidean Lie-algebra respecting different types of PT-symmetries, we find explicit solutions to the time-dependent Dyson equation. A specific Hermitian model with explicit time-dependence is analyzed further and shown to be quasi-exactly solvable. Technically we constructed the Lewis–Riesenfeld invariants making use of the metric picture, which is an equivalent alternative to the Schrödinger, Heisenberg and interaction picture containing the time-dependence in the metric operator that relates the time-dependent Hermitian Hamiltonian to a static non-Hermitian Hamiltonian.     

The fermion density operator in the droplet bosonization picture

We derive the phase space particle density operator in the ‘droplet’ picture of bosonization in terms of the boundary operator. We demonstrate that it satisfies the correct algebra and acts on the proper Hilbert space describing the underlying fermion system, and therefore it can be used to bosonize any Hamiltonian or related operator. As a demonstration we show that it reproduces the correct excitation energies for a system of free fermions with arbitrary dispersion relations.     

Spatial screening solitons as particles

Photorefractive spatial screening solitons are treated as rays using geometrical optics. The ray picture is transformed into a classical mechanics picture, in which solitons move self-consistently as particles in a potential created by the induced change in the refractive index. The Hamiltonian equations of motion are integrated to yield trajectories that agree with the optical center-of-mass trajectories. The motion in the transverse plane is found to be not central and the orbits are not closed, preventing the spiraling of solitons.     

Preparation of the Cluster States in a Linear Trap Systems

A scheme for the preparation of four-ion entangled cluster states has been proposed. Two two-level ions are confined in a linear trap and are simultaneously driven with a laser beam. In the Lamb-Dicke regime, we can get the effective Hamiltonian in the interaction picture.The effective Hamiltonian may be used to describe a realistic physical system. The scheme is insensitive to both the initial vibrational state and heating.     

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators.     

Primordial power spectrum from the Dapor–Liegener model of loop quantum cosmology

We compute the predictions for the power spectrum of scalar perturbations from a recent new proposal for the effective Hamiltonian of loop quantum cosmology. The model provides an attractive picture of the early cosmos, in which our classical Friedmann–Lemaître–Robertson–Walker universe emerges from a quantum phase where the spacetime curvature remains constant and of Planckian size. We compare the predictions for the cosmic microwave background with previous results obtained within loop quantum cosmology, and discuss the differences and similarities. The analysis provides an example of the way differences between quantization schemes can be translated to physical observables.     

AlN, GaN and InN (0 0 1) surface electronic band structure

We have studied the electronic band structure of the ideal (0 0 1) surface of AlN, GaN and InN in the zinc-blende phase. We have employed an empirical sp³s^∗d⁵ Hamiltonian with nearest-neighbor interactions including spin-orbit coupling and the surface Green function matching method. We have obtained the different surface states together with their corresponding orbital character and localization in the different layers. A similar physical picture is obtained for the three materials.     

Feynman formulas and path integrals for some evolution semigroups related to τ-quantization

This note is devoted to Feynman formulas (i.e., representations of semigroups by limits of n-fold iterated integrals as n → ∞) and their connections with phase space Feynman path integrals. Some pseudodifferential operators corresponding to different types of quantization of a quadratic Hamiltonian function are considered. Lagrangian and Hamiltonian Feynman formulas for semigroups generated by these operators are obtained. Further, a construction of Hamiltonian (phase space) Feynman path integrals is introduced. Due to this construction, the Hamiltonian Feynman formulas obtained here and in our previous papers do coincide with Hamiltonian Feynman path integrals. This connects phase space Feynman path integrals with some integrals with respect to probability measures. These connections enable us to make a contribution to the theory of phase space Feynman path integrals, to prove the existence of some of these integrals, and to study their properties by means of stochastic analysis. The Feynman path integrals thus obtained are different for different types of quantization. This makes it possible to distinguish the process of quantization in the language of Feynman path integrals.     

Nonadiabatic Quantum Search Algorithm with Analytical Success Rate

In nonadiabatic quantum search algorithm, it is difficult to calculate the success rate analytically. We develop the nonadiabatic quantum search algorithm by adding a counterdiabatic driving term to the original time-dependent Hamiltonian. The Hamiltonian we structured is diagonal in eigen picture and the time-independent Schrödinger equation is solved analytically. Then, we get an accurate analytical expression of success rate in nonadiabatic quantum search algorithm. Utilizing this expression, a sufficient condition, which can ensure the success rate be one with arbitrary evolution time, was found. Moreover, we can choose the better parameters by calculating the precise success rate according to the expression.

     

“Eigen-Operator” Method of the Square of Schroedinger Operator in Interaction Picture and Its Application in Describing Parametric Amplifiers

We extend the method of searching “eigen-operator” of the square of the Schroedinger operator to the interaction picture, which not only helps to construct Hamiltonians of two kinds of parametric amplifiers but also leads to a new uncertainty relation regarding to the free Hamiltonian and the interacting Hamiltonian.     

Matrix Algebras in Non-Hermitian Quantum Mechanics

In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schrödinger's picture of quantum dynamics. Here it is shown in both cases how to map the algebra of commutators, defining the time evolution in terms of a non-Hermitian Hamiltonian, onto a non-Hamiltonian algebra with a Hermitian Hamiltonian. The logic behind such a derivation is reversible, so that any Hermitian Hamiltonian can be used in the formulation of non-Hermitian dynamics through a suitable algebra of generalized (non-Hamiltonian) commutators.
These results provide a general structure (a template) for non-Hermitian equations of motion to be used in the computer simulation of open quantum systems dynamics.