arXiv subjects

T. Gorin

Publications and source records attributed to T. Gorin.

At least 19 recordsLinked to original sources

arXiv2020

Sound field radiated by a rod

We study the acoustical intensity field radiated by a thin cylindrical rod vibrating in its lowest compressional mode. Due to the cylindrical symmetry, the emitted field is measured in a radial plane of the rod which is sufficient to reconstruct the full three-dimensional field. Starting from the one-dimensional approximation of the excited compressional mode, we develop a simplified theoretical wave equation which allows for a semi-analytical solution for the emitted wave field. The agreement between the experimental results and the semi-analytical solution is eloquent.

physics.app-ph↗

arXiv2019

Markovian and non-Markovian dynamics induced by a generic environment

We study the open dynamics of a quantum two-level system coupled to an environment modeled by random matrices. Using the quantum channel formalism, we investigate different quantum Markovianity measures and criteria. A thorough analysis of the whole parameter space, reveals a wide range of different regimes, ranging from strongly non-Markovian to Markovian dynamics. In contrast to analytical models, all non-Markovianity measures and criteria have to be applied to data with fluctuations and statistical uncertainties. We discuss the practical usefulness of the different approaches.

quant-ph↗

arXiv2016

Quantum kicked harmonic oscillator in contact with a heat bath

We consider the quantum harmonic oscillator in contact with a finite temperature bath, modelled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system in different dynamical regimes between classical integrability and chaos on the one hand, and ballistic or diffusive energy absorption on the other. We then investigate the influence of the heat bath on the oscillator in each case. Phase space techniques allow us to simulate the evolution of the system efficiently. In this way, we calculate high resolution Wigner functions at long times, where the system approaches a quasi-stationary cyclic evolution. Thereby, we are able to perform an accurate study of the thermodynamic properties of a non-integrable, quantum chaotic system in contact with a heat bath.

quant-ph↗

arXiv2015

Joint probability distributions for projection probabilities of random orthonormal states

A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different probabilities for obtaining a specific outcome in a projective measurement, provided the system is in one of its eigenstates. We then give analytic expressions for the joint probability density for these probabilities, with respect to the ensemble of random matrices. In the case of the unitary group, our results can be applied, also, to the phenomenon of universal conductance fluctuations, where the same mathematical quantities describe partial conductances in a two-terminal mesoscopic scattering problem with a finite number of modes in each terminal.

math-ph↗

arXiv2015

Improving coherence with nested environments

We have in mind a register of qubits for an quantum information system, and consider its decoherence in an idealized but typical situation. Spontaneous decay and other couplings to the far environment considered as the world outside the quantum apparatus will be neglected, while couplings to quantum states within the apparatus, i.e. to a near environment are assumed to dominate. Thus the central system couples to the near environment which in turn couples to a far environment. Considering that the dynamics in the near environment is not sufficiently well known or controllable, we shall use random matrix methods to obtain analytic results. We consider a simplified situation where the central system suffers weak dephasing from the near environment, which in turn is coupled randomly to the far environment. We find the anti-intuitive result that increasing the coupling between near and far environment actually protects the central qubit.

quant-ph↗

arXiv2014

Single qubit decoherence under a separable coupling to a random matrix environment

This paper describes the dynamics of a quantum two-level system (qubit) under the influence of an environment modeled by an ensemble of random matrices. In distinction to earlier work, we consider here separable couplings and focus on a regime where the decoherence time is of the same order of magnitude than the environmental Heisenberg time. We derive an analytical expression in the linear response approximation, and study its accuracy by comparison with numerical simulations. We discuss a series of unusual properties, such as purity oscillations, strong signatures of spectral correlations (in the environment Hamiltonian), memory effects and symmetry breaking equilibrium states.

quant-ph↗

arXiv2012

Scattering approach to fidelity decay in closed systems and parametric level correlations

This paper is based on recent work which provided an exact analytical description of scattering fidelity experiments with a microwave cavity under the variation of an antenna coupling [Köber et al., Phys. Rev. E 82, 036207 (2010)]. It is shown that this description can also be used to predict the decay of the fidelity amplitude for arbitrary Hermitian perturbations of a closed system. Two applications are presented: First, the known result for global perturbations is re-derived, and second, the exact analytical expression for the perturbation due to a moving S-wave scatterer is worked out. The latter is compared to measured data from microwave experiments, which have been reported some time ago. Finally, we generalize an important relation between fidelity decay and parametric level correlations to arbitrary perturbations.

nlin.CD↗

arXiv2010

Microwave fidelity studies by varying antenna coupling

The fidelity decay in a microwave billiard is considered, where the coupling to an attached antenna is varied. The resulting quantity, coupling fidelity, is experimentally studied for three different terminators of the varied antenna: a hard wall reflection, an open wall reflection, and a 50 Ohm load, corresponding to a totally open channel. The model description in terms of an effective Hamiltonian with a complex coupling constant is given. Quantitative agreement is found with the theory obtained from a modified VWZ approach [Verbaarschot et al, Phys. Rep. 129, 367 (1985)].

nlin.CD↗

arXiv2009

Simulation of static and random errors on Grover's search algorithm implemented in a Ising nuclear spin chain quantum computer with few qubits

We consider Grover's search algorithm on a model quantum computer implemented on a chain of four or five nuclear spins with first and second neighbour Ising interactions. Noise is introduced into the system in terms of random fluctuations of the external fields. By averaging over many repetitions of the algorithm, the output state becomes effectively a mixed state. We study its overlap with the nominal output state of the algorithm, which is called fidelity. We find either an exponential or a Gaussian decay for the fidelity as a function of the strength of the noise, depending on the type of noise (static or random) and whether error supression is applied (the 2pi k-method) or not.

quant-ph↗

arXiv2008

A random matrix theory of decoherence

Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix arising from the ensemble induced, in contrast to previous studies where the average values of purity, concurrence, and entropy were considered; we further discuss when one or the other approach is relevant. The two approaches agree in the limit of large environments. Analytic results for the average density matrix and its purity are presented in linear response approximation. The two-qubit system is analysed, mainly numerically, in more detail.

quant-ph↗

arXiv2007

Monomial integrals on the classical groups

This paper presents a powerfull method to integrate general monomials on the classical groups with respect to their invariant (Haar) measure. The method has first been applied to the orthogonal group in [J. Math. Phys. 43, 3342 (2002)], and is here used to obtain similar integration formulas for the unitary and the unitary symplectic group. The integration formulas turn out to be of similar form. They are all recursive, where the recursion parameter is the number of column (row) vectors from which the elements in the monomial are taken. This is an important difference to other integration methods. The integration formulas are easily implemented in a computer algebra environment, which allows to obtain analytical expressions very efficiently. Those expressions contain the matrix dimension as a free parameter.

math-ph↗

arXiv2007

Simulation of Grover's quantum search algorithm in a Ising nuclear spin chain quantum computer with first and second nearest neighbour couplings

We implement Grover's quantum search algorithm on a nuclear spin chain quantum computer, taking into Ising type interactions between nearest and second nearest neighbours into account. The performance of the realisation of the algorithm is studied by numerical simulations with four spins. We determine the temporal behaviour of the fidelity during the algorithm, and we compute the final fidelity as a function of the Rabi frequency. For the latter, we obtained pronounced maxima at frequencies which fulfil the condition of the (2πk)-method with respect to the second nearest neighbour interactions.

quant-ph↗

arXiv2007

Quantum computation in a Ising spin chain taking into account second neighbor couplings

We consider the realization of a quantum computer in a chain of nuclear spins coupled by an Ising interaction. Quantum algorithms can be performed with the help of appropriate radio-frequency pulses. In addition to the standard nearest-neighbor Ising coupling, we also allow for a second neighbor coupling. It is shown, how to apply the 2πk method in this more general setting, where the additional coupling eventually allows to save a few pulses. We illustrate our results with two numerical simulations: the Shor prime factorization of the number 4 and the teleportation of a qubit along a chain of 3 qubits. In both cases, the optimal Rabi frequency (to suppress non-resonant effects) depends primarily on the strength of the second neighbor interaction.

quant-ph↗

arXiv2007

Decoherence of two qubit systems: A random matrix description

We study decoherence of two non-interacting qubits. The environment and its interaction with the qubits are modelled by random matrices. Decoherence, measured in terms of purity, is calculated in linear response approximation. Monte Carlo simulations illustrate the validity of this approximation and of its extension by exponentiation. The results up to this point are also used to study one qubit decoherence. Purity decay of entangled and product states are qualitatively similar though for the latter case it is slower. Numerical studies for a Bell pair as initial state reveal a one to one correspondence between its decoherence and its internal entanglement decay. For strong and intermediate coupling to the environment this correspondence agrees with the one for Werner states. In the limit of a large environment the evolution induces a unital channel in the two qubits, providing a partial explanation for the relation above.

quant-ph↗

arXiv2006

Long-time signatures of short-time dynamics in decaying quantum-chaotic systems

We analyze the decay of classically chaotic quantum systems in the presence of fast ballistic escape routes on the Ehrenfest time scale. For a continuous excitation process, the form factor of the decay cross section deviates from the universal random-matrix result on the Heisenberg time scale, i.e. for times much larger than the time for ballistic escape. We derive an exact analytical description and compare our results with numerical simulations for a dynamical model.

nlin.CD↗

arXiv2006

Anomalous slow fidelity decay for symmetry breaking perturbations

Symmetries as well as other special conditions can cause anomalous slowing down of fidelity decay. These situations will be characterized, and a family of random matrix models to emulate them generically presented. An analytic solution based on exponentiated linear response will be given. For one representative case the exact solution is obtained from a supersymmetric calculation. The results agree well with dynamical calculations for a kicked top.

nlin.CD↗

arXiv2005

Random matrix description of decaying quantum systems

This contribution describes a statistical model for decaying quantum systems (e.g. photo-dissociation or -ionization). It takes the interference between direct and indirect decay processes explicitely into account. The resulting expressions for the partial decay amplitudes and the corresponding cross sections may be considered a many-channel many-resonance generalization of Fano's original work on resonance lineshapes [Phys. Rev 124, 1866 (1961)]. A statistical (random matrix) model is then introduced. It allows to describe chaotic scattering systems with tunable couplings to the decay channels. We focus on the autocorrelation function of the total (photo) cross section, and we find that it depends on the same combination of parameters, as the Fano-parameter distribution. These combinations are statistical variants of the one-channel Fano parameter. It is thus possible to study Fano interference (i.e. the interference between direct and indirect decay paths) on the basis of the autocorrelation function, and thereby in the regime of overlapping resonances. It allows us, to study the Fano interference in the limit of strongly overlapping resonances, where we find a persisting effect on the level of the weak localization correction.

nlin.CD↗

arXiv2005

Experimental verification of fidelity decay: From perturbative to Fermi Golden Rule regime

The scattering matrix was measured for a flat microwave cavity with classically chaotic dynamics. The system can be perturbed by small changes of the geometry. We define the "scattering fidelity" in terms of parametric correlation functions of scattering matrix elements. In chaotic systems and for weak coupling the scattering fidelity approaches the fidelity of the closed system. Without free parameters the experimental results agree with random matrix theory in a wide range of perturbation strengths, reaching from the perturbative to the Fermi golden rule regime.

nlin.CD↗