Quantum noise in the electromechanical shuttle: Quantum master equation treatment

We consider a type of quantum electromechanical system, known as the shuttle system, first proposed by Gorelik [Phys. Rev. Lett. 80, 4526 (1998)]. We use a quantum master equation treatment and compare the semiclassical solution to a full quantum simulation to reveal the dynamics, followed by a discussion of the current noise of the system. The transition between tunneling and shuttling regime can be measured directly in the spectrum of the noise. (c) 2006 American Institute of Physics.

Studies on Wilson loops, correlators and localization in supersymmetric quantum field theories

In this thesis we study at perturbative level correlation functions of Wilson loops (and local operators) and their relations to localization, integrability and other quantities of interest as the cusp anomalous dimension and the Bremsstrahlung function. First of all we consider a general class of 1/8 BPS Wilson loops and chiral primaries in N=4 Super Yang-Mills theory. We perform explicit two-loop computations, for some particular but still rather general configuration, that confirm the elegant results expected from localization procedure. We find notably full consistency with the multi-matrix model averages, obtained from 2D Yang-Mills theory on the sphere, when interacting diagrams do not cancel and contribute non-trivially to the final answer. We also discuss the near BPS expansion of the generalized cusp anomalous dimension with L units of R-charge. Integrability provides an exact solution, obtained by solving a general TBA equation in the appropriate limit: we propose here an alternative method based on supersymmetric localization. The basic idea is to relate the computation to the vacuum expectation value of certain 1/8 BPS Wilson loops with local operator insertions along the contour. Also these observables localize on a two-dimensional gauge theory on S^2, opening the possibility of exact calculations. As a test of our proposal, we reproduce the leading Luscher correction at weak coupling to the generalized cusp anomalous dimension. This result is also checked against a genuine Feynman diagram approach in N=4 super Yang-Mills theory. Finally we study the cusp anomalous dimension in N=6 ABJ(M) theory, identifying a scaling limit in which the ladder diagrams dominate. The resummation is encoded into a Bethe-Salpeter equation that is mapped to a Schroedinger problem, exactly solvable due to the surprising supersymmetry of the effective Hamiltonian. In the ABJ case the solution implies the diagonalization of the U(N) and U(M) building blocks, suggesting the existence of two independent cusp anomalous dimensions and an unexpected exponentation structure for the related Wilson loops.

Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90

Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics

Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.

Quantum transition state theory and solving a first order master equation for complex reactions numerically

The field of chemical kinetics is an exciting and active field. The prevailing theories make a number of simplifying assumptions that do not always hold in actual cases. Another current problem concerns a development of efficient numerical algorithms for solving the master equations that arise in the description of complex reactions. The objective of the present work is to furnish a completely general and exact theory of reaction rates, in a form reminiscent of transition state theory, valid for all fluid phases and also to develop a computer program that can solve complex reactions by finding the concentrations of all participating substances as a function of time. To do so, the full quantum scattering theory is used for deriving the exact rate law, and then the resulting cumulative reaction probability is put into several equivalent forms that take into account all relativistic effects if applicable, including one that is strongly reminiscent of transition state theory, but includes corrections from scattering theory. Then two programs, one for solving complex reactions, the other for solving first order linear kinetic master equations to solve them, have been developed and tested for simple applications.

Dynamic polarizability, Cauchy moments, and the optical absorption spectrum of liquid water: A sequential molecular dynamics/quantum mechanical approach

The dynamic polarizability and optical absorption spectrum of liquid water in the 6-15 eV energy range are investigated by a sequential molecular dynamics (MD)/quantum mechanical approach. The MD simulations are based on a polarizable model for liquid water. Calculation of electronic properties relies on time-dependent density functional and equation-of-motion coupled-cluster theories. Results for the dynamic polarizability, Cauchy moments, S(-2), S(-4), S(-6), and dielectric properties of liquid water are reported. The theoretical predictions for the optical absorption spectrum of liquid water are in good agreement with experimental information.

Nonlinear transport and oscillating magnetoresistance in double quantum wells

The nonlinear regime of low-temperature magnetoresistance of double quantum wells in the region of magnetic fields below 1 T is studied both experimentally and theoretically. The observed inversion of the magnetointersubband oscillation peaks with increasing electric current and splitting of these peaks are described by the theory based on the kinetic equation for the isotropic nonequilibrium part of electron distribution function. The inelastic-scattering time of electrons is determined from the current dependence of the inversion field.

Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space

We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a theta modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the theta-modified Dirac equation. To complete the consideration, we present a pseudoclassical model (a la Berezin-Marinov) for the corresponding nonrelativistic particle in the noncommutative space. To justify the latter model, we demonstrate that its quantization leads to the theta-modified Pauli equation. We extract theta-modified interaction between a nonrelativistic spin and a magnetic field from such a Pauli equation and construct a theta modification of the Heisenberg model for two coupled spins placed in an external magnetic field. In the framework of such a model, we calculate the probability transition between two orthogonal Einstein-Podolsky-Rosen states for a pair of spins in an oscillatory magnetic field and show that some of such transitions, which are forbidden in the commutative space, are possible due to the space noncommutativity. This allows us to estimate an upper bound on the noncommutativity parameter.

Extending Bell's beables to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories

In this paper, employing the Ito stochastic Schrodinger equation, we extend Bell's beable interpretation of quantum mechanics to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories. For a particular choice of the source of stochasticity, the one leading to a dissipative Lindblad-type correction to the Hamiltonian dynamics, we find that the diffusive terms in Nelsons stochastic trajectories are naturally incorporated into Bohm's causal dynamics, yielding a unified Bohm-Nelson theory. In particular, by analyzing the interference between quantum trajectories, we clearly identify the decoherence time, as estimated from the quantum formalism. We also observe the quantum-to-classical transition in the convergence of the infinite ensemble of quantum trajectories to their classical counterparts. Finally, we show that our extended beables circumvent the problems in Bohm's causal dynamics regarding stationary states in quantum mechanics.

Reverse engineering in many-body quantum physics: Correspondence between many-body systems and effective single-particle equations

The mapping, exact or approximate, of a many-body problem onto an effective single-body problem is one of the most widely used conceptual and computational tools of physics. Here, we propose and investigate the inverse map of effective approximate single-particle equations onto the corresponding many-particle system. This approach allows us to understand which interacting system a given single-particle approximation is actually describing, and how far this is from the original physical many-body system. We illustrate the resulting reverse engineering process by means of the Kohn-Sham equations of density-functional theory. In this application, our procedure sheds light on the nonlocality of the density-potential mapping of density-functional theory, and on the self-interaction error inherent in approximate density functionals.

Dynamical quantum noise in trapped Bose-Einstein condensates

We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We derive evolution equations for a single trapped condensate in both the positive-P and Wigner representations and perform simulations to compare the predictions of the two methods. The positive-P approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial stare for the condensate and compare results to those for single-mode models. [S1050-2947(98)06612-8].

Quantum open-systems approach to current noise in resonant tunneling junctions

A quantum Markovian master equation is derived to describe the current noise in resonant tunneling devices. This equation includes both incoherent and coherent quantum tunneling processes. We show how to obtain the population master equation by adiabatic elimination of quantum coherences in the presence of elastic scattering. We calculate the noise spectrum for a double well device and predict subshot noise statistics for strong tunneling between the wells. The method is an alternative to Green's function methods and population master equations for very small coherently coupled quantum dots.

Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field

We present some exact results for the effect of disorder on the critical properties of an anisotropic XY spin chain in a transverse held. The continuum limit of the corresponding fermion model is taken and in various cases results in a Dirac equation with a random mass. Exact analytic techniques can then be used to evaluate the density of states and the localization length. In the presence of disorder the ferromagnetic-paramagnetic or Ising transition of the model is in the same universality class as the random transverse field Ising model solved by Fisher using a real-space renormalization-group decimation technique (RSRGDT). If there is only randomness in the anisotropy of the magnetic exchange then the anisotropy transition (from a ferromagnet in the x direction to a ferromagnet in the y direction) is also in this universality class. However, if there is randomness in the isotropic part of the exchange or in the transverse held then in a nonzero transverse field the anisotropy transition is destroyed by the disorder. We show that in the Griffiths' phase near the Ising transition that the ground-state energy has an essential singularity. The results obtained for the dynamical critical exponent, typical correlation length, and for the temperature dependence of the specific heat near the Ising transition agree with the results of the RSRODT and numerical work. [S0163-1829(99)07125-8].

A new approach to current and noise in double quantum dot systems

We use a quantum master equation to describe transport in double-dot devices. The coherent dot-to-dot coupling affects the noise spectra strongly. For phonon-assisted tunneling, the calculated current spectra are consistent with those of experiments. The model shows that quantum stochastic theory may he applied to some advantage in mesoscopic electronic systems. (C) 2000 Elsevier Science B.V. All rights reserved.

Quantum interference in the fluorescence of a molecular system

It has been observed experimentally [H.R. Xia, C.Y. Ye, and S.Y. Zhu, Phys. Rev. Lett. 77, 1032 (1996)] that quantum interference between two molecular transitions can lead to a suppression or enhancement of spontaneous emission. This is manifest in the fluorescent intensity as a function of the detuning of the driving field from the two-photon resonance condition. Here we present a theory that explains the observed variation of the number of peaks with the mutual polarization of the molecular transition dipole moments. Using master equation techniques we calculate analytically as well as numerically the steady-state fluorescence, and find that the number of peaks depends on the excitation process. If the molecule is driven to the upper levels by a two-photon process, the fluorescent intensity consists of two peaks regardless of the mutual polarization of the transition dipole moments. Lf the excitation process is composed of both a two-step, one-photon process and a one-step, two-photon process, then there are two peaks on transitions with parallel dipole moments and three peaks on transitions with antiparallel dipole moments. This latter case is in excellent agreement with the experiment.