arXiv subjects

Thomas H. Seligman

Publications and source records attributed to Thomas H. Seligman.

At least 37 records · Page 2Linked to original sources

arXiv2016

Microwave emulations and tight-binding calculations of transport in polyacetylene

A novel approach to investigate the electron transport of cis- and trans-polyacetylene chains in the single-electron approximation is presented by using microwave emulation measurements and tight-binding calculations. In the emulation we take into account the different electronic couplings due to the double bonds leading to coupled dimer chains. The relative coupling constants are adjusted by DFT calculations. For sufficiently long chains a transport band gap is observed if the double bonds are present, whereas for identical couplings no band gap opens. The band gap can be observed also in relatively short chains, if additional edge atoms are absent, which cause strong resonance peaks within the band gap. The experimental results are in agreement with our tight-binding calculations using the nonequilibrium Green's function method. The tight-binding calculations show that it is crucial to include third nearest neighbor couplings to obtain the gap in the cis-polyacetylene.

cond-mat.mes-hall↗

arXiv2015

Random density matrices versus random evolution of open systems

We present and compare two families of ensembles of random density matrices. The first, static ensemble, is obtained foliating an unbiased ensemble of density matrices. As criterion we use fixed purity as the simplest example of a useful convex function. The second, dynamic ensemble, is inspired in random matrix models for decoherence where one evolves a separable pure state with a random Hamiltonian until a given value of purity in the central system is achieved. Several families of Hamiltonians, adequate for different physical situations, are studied. We focus on a two qubit central system, and obtain exact expressions for the static case. The ensemble displays a peak around Werner-like states, modulated by nodes on the degeneracies of the density matrices. For moderate and strong interactions good agreement between the static and the dynamic ensembles is found. Even in a model where one qubit does not interact with the environment excellent agreement is found, but only if there is maximal entanglement with the interacting one. The discussion is started recalling similar considerations for scattering theory. At the end, we comment on the reach of the results for other convex functions of the density matrix, and exemplify the situation with the von Neumann entropy.

quant-ph↗

arXiv2015

A generalized fidelity amplitude for open systems

We consider a central system which is coupled via dephasing to an open system, i.e. an intermediate system which in turn is coupled to another environment. Considering intermediate and far environment as one composite system, the coherences in the central system are given in the form of fidelity amplitudes for a certain perturbed echo dynamics in the composite environment. On the basis of the Born-Markov approximation, we derive a master equation for the reduction of that dynamics to the intermediate system alone. In distinction to an earlier paper [arXiv: 1502.04143 (2015)] where we discussed the stabilizing effect of the far environment on the decoherence in the central system, we focus here on the possibility to use the measurable coherences in the central system for probing the open quantum dynamics in the intermediate system. We illustrate our results for the case of chaotic dynamics in the near environment, where we compare random matrix simulations with our analytical result.

quant-ph↗

arXiv2013

Time series, correlation matrices and random matrix models

In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null hypothesis or a minimum information hypothesis for the description of a quantum system or subsystem. In the former case various forms of correlation matrices of time series associated with the classical observables of some system. The fact that such series are necessarily finite, inevitably introduces noise and this finite time influence lead to a random or stochastic component in these time series. By consequence random correlation matrices have a random component, and corresponding ensembles are used. In the latter we use random matrices to describe high temperature environment or uncontrolled perturbations, ensembles of differing chaotic systems etc.

math-ph↗

arXiv2013

Emerging spectra of singular correlation matrices under small power-map deformations

Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used this implies an analysis of highly singular correlation matrices. We attack this problem by using the so called {\it power map} which was introduced to reduce noise. Its non-linearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

math-ph↗

arXiv2011

Decoherence at constant excitation

We present a simple exactly solvable extension of of the Jaynes-Cummings model by adding dissipation. This is done such that the total number of excitations is conserved. The Liouville operator in the resulting master equation can be reduced to blocks of $4\times 4$ matrices.

quant-ph↗

arXiv2011

Fourier's Law for Quasi One--Dimensional Chaotic Quantum Systems

We derive Fourier's law for a completely coherent quasi one--dimensional chaotic quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the level density and, thus, inversely proportional to the length of the system.

quant-ph↗

arXiv2011

Fidelity decay in interacting two-level boson systems: Freezing and revivals

We study the fidelity decay in the $k$-body embedded ensembles of random matrices for bosons distributed in two single-particle states, considering the reference or unperturbed Hamiltonian as the one-body terms and the diagonal part of the $k$-body embedded ensemble of random matrices, and the perturbation as the residual off-diagonal part of the interaction. We calculate the ensemble-averaged fidelity with respect to an initial random state within linear response theory to second order on the perturbation strength, and demonstrate that it displays the freeze of the fidelity. During the freeze, the average fidelity exhibits periodic revivals at integer values of the Heisenberg time $t_H$. By selecting specific $k$-body terms of the residual interaction, we find that the periodicity of the revivals during the freeze of fidelity is an integer fraction of $t_H$, thus relating the period of the revivals with the range of the interaction $k$ of the perturbing terms. Numerical calculations confirm the analytical results.

nlin.CD↗

arXiv2010

Third quantization

The basic ideas of second quantization and Fock space are extended to density operator states, used in treatments of open many-body systems. This can be done for fermions and bosons. While the former only requires the use of a non-orthogonal basis, the latter requires the introduction of a dual set of spaces. In both cases an operator algebra closely resembling the canonical one is developed and used to define the dual sets of bases. We here concentrated on the bosonic case where the unboundedness of the operators requires the definitions of dual spaces to support the pair of bases. Some applications, mainly to non-equilibrium steady states, will be mentioned.

quant-ph↗

arXiv2010

Fidelity decay of the two-level bosonic embedded ensembles of Random Matrices

We study the fidelity decay of the $k$-body embedded ensembles of random matrices for bosons distributed over two single-particle states. Fidelity is defined in terms of a reference Hamiltonian, which is a purely diagonal matrix consisting of a fixed one-body term and includes the diagonal of the perturbing $k$-body embedded ensemble matrix, and the perturbed Hamiltonian which includes the residual off-diagonal elements of the $k$-body interaction. This choice mimics the typical mean-field basis used in many calculations. We study separately the cases $k=2$ and $3$. We compute the ensemble-averaged fidelity decay as well as the fidelity of typical members with respect to an initial random state. Average fidelity displays a revival at the Heisenberg time, $t=t_H=1$, and a freeze in the fidelity decay, during which periodic revivals of period $t_H$ are observed. We obtain the relevant scaling properties with respect to the number of bosons and the strength of the perturbation. For certain members of the ensemble, we find that the period of the revivals during the freeze of fidelity occurs at fractional times of $t_H$. These fractional periodic revivals are related to the dominance of specific $k$-body terms in the perturbation.

quant-ph↗

arXiv2010

The Dirac-Moshinsky oscillator coupled to an external field and its connection to quantum optics

The Dirac-Moshinsky oscillator is an elegant example of an exactly solvable quantum relativistic model that under certain circumstances can be mapped onto the Jaynes-Cummings model in quantum optics. In this work we show, how to do this in detail. Then we extend it by considering its coupling with an external (isospin) field and find the conditions that maintain solvability. We use this extended system to explore entanglement in relativistic systems and then identify its quantum optical analog: two different atoms interacting with an electromagnetic mode. We show different aspects of entanglement which gain relevance in this last system, which can be used to emulate the former.

quant-ph↗

arXiv2010

Spontaneous symmetry breaking by double lithium adsorption in polyacenes

We show that adsorption of one lithium atom to a polyacenes, i.e. chains of linearly fused benzene rings, will cause this chain to be slightly deformed. If we adsorb a second identical atom on the opposite side of the same ring, this deformation is dramatically enhanced despite of the fact, that a symmetric configuration seems possible. We argue, that this may be due to an instability of the Jahn-Teller type possibly indeed to a Peierls instability.

physics.chem-ph↗

arXiv2010

Quantization over boson operator spaces

The framework of third quantization - canonical quantization in the Liouville space - is developed for open many-body bosonic systems. We show how to diagonalize the quantum Liouvillean for an arbitrary quadratic n-boson Hamiltonian with arbitrary linear Lindblad couplings to the baths and, as an example, explicitly work out a general case of a single boson.

quant-ph↗

arXiv2010

Dynamics of a Dirac oscillator coupled to an external field: A new class of solvable problems

The Dirac oscillator coupled to an external two-component field can retain its solvability, if couplings are appropriately chosen. This provides a new class of integrable systems. A simplified way of solution is given, by recasting the known solution of the Dirac oscillator into matrix form; there one notices, that a block-diagonal form arises in a Hamiltonian formulation. The blocks are two-dimensional. Choosing couplings that do not affect the block structure, these just blow up the $2 \times 2$ matrices to $4 \times 4 $ matrices, thus conserving solvability. The result can be cast again in covariant form. By way of example we apply this exact solution to calculate the evolution of entanglement.

quant-ph↗

arXiv2008

About Imperfect Mushroom Billiards

Imperfections of Bunimovich mushroom Billiards are analyzed. Any experiment will be affected by such imperfections, and it will be necessary to estimate their influence. In particular some of the corners will be rounded and small deviations of the angle of the underside of the mushroom head will be considered. The analysis displayed some unexpected non-generic features. The latter leads to a transition from a perfect mushroom behavior to either an ordinary KAM scenario or an abrupt transition to complete chaos, depending on the sign of the perturbation. The former produces a fractal area of islands and chaos, in fact a KAM scenario, not associated to the large island of stability of the mushroom billiard.

nlin.CD↗

arXiv2008

Relativistic echo dynamics and the stability of a beam of Landau electrons

We extend the concepts of echo dynamics and fidelity decay to relativistic quantum mechanics, specifically in the context of Klein-Gordon and Dirac equations under external electromagnetic fields. In both cases we define similar expressions for the fidelity amplitude under perturbations of these fields, and a covariant version of the echo operator. Transformation properties under the Lorentz group are established. An alternate expression for fidelity is given in the Dirac case in terms of a 4-current. As an application we study a beam of Landau electrons perturbed by field inhomogeneities.

quant-ph↗

arXiv2008

Electron Localization on Molecular Surfaces by Metal Adsorption

The ability of metal adsorption to transfer charge to the surface of single molecular carbon sheets is explored in this paper. Though other metals are considered we basically will deal with Lithium We concentrate on fairly small sheets and examined the minimum threshold size of a molecular surface needed to separate metals. From our quantum chemical calculations we deduce that a molecular surface of six benzene rings is needed for Lithium dimers to be separated. We further observe symmetry breaking, when two lithium atoms are adsorbed right opposite to each other on the two sides of the sheet.

cond-mat.mtrl-sci↗

arXiv2007

Random matrix models for decoherence and fidelity decay in quantum information systems

This course aims to introduce the student to random matrix models for decoherence and fidelity decay. They present a very powerful alternate approach, that emphasizes the disordered character of many environments and uncontrollable perturbations/couplings. The inherent integrability of such models makes analytic studies possible. We limit our considerations to linear response treatment, as high fidelity and small decoherence are the backbone of quantum information processes. For fidelity decay, where experimental results are available, a comparison with experiments shows excellent agreement with random matrix theory predictions.

quant-ph↗