Biomedical subjects

F M Izrailev

Publications and source records attributed to F M Izrailev.

10 recordsLinked to original sources

PubMed2002

Dynamical fidelity of a solid-state quantum computation.

In this paper we analyze the dynamics in a spin model of quantum computer. Main attention is paid to the dynamical fidelity (associated with dynamical errors) of an algorithm that allows to create an entangled state for remote qubits. We show that in the regime of selective resonant excitations of qubits there is no danger of quantum chaos. Moreover, in this regime a modified perturbation theory gives an adequate description of the dynamics of the system. Our approach allows us to explicitly describe all peculiarities of the evolution of the system under time-dependent pulses corresponding to a quantum protocol. Specifically, we analyze, both analytically and numerically, how the fidelity decreases in dependence on the model parameters.

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PubMed2002

Quantum Arnol'd diffusion in a simple nonlinear system.

We study the fingerprint of the Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators with a two-frequency external force. In the classical description, this peculiar diffusion is due to the onset of a weak chaos in a narrow stochastic layer near the separatrix of the coupling resonance. We have found that global dependence of the quantum diffusion coefficient on model parameters mimics, to some extent, the classical data. However, the quantum diffusion happens to be slower than the classical one. Another result is the dynamical localization that leads to a saturation of the diffusion after some characteristic time. We show that this effect has the same nature as for the studied earlier dynamical localization in the presence of global chaos. The quantum Arnol'd diffusion represents a new type of quantum dynamics and can be observed, for example, in two-dimensional semiconductor structures (quantum billiards) perturbed by time-periodic external fields.

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PubMed2002

Manifestation of Arnol'd diffusion in quantum systems.

We study an analog of the classical Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators one of which is governed by an external periodic force with two frequencies. In a classical model this very weak diffusion happens in a narrow stochastic layer along the coupling resonance and leads to an increase of the total energy of the system. We show that quantum dynamics of wave packets mimics, up to some extent, global properties of the classical Arnol'd diffusion. This specific diffusion represents a new type of quantum dynamics and may be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.

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PubMed2002

Semiquantal approach to finite systems of interacting particles.

A novel approach is suggested for the statistical description of quantum systems of interacting particles. We show that the occupation numbers for single-particle states can be represented as a convolution of a classical analog of the eigenstate, with the quantum occupation number for noninteracting particles. The latter takes into account the wave function symmetry and depends on the unperturbed energy spectrum only. As a result, the distribution of occupation numbers n(s) can be found even for a large number of interacting particles. Using the model of interacting spins, we demonstrate that this approach gives a correct description of n(s) even in deep quantum regions with few single-particle orbitals.

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PubMed2001

Avoiding quantum chaos in quantum computation.

We study a one-dimensional chain of nuclear 1/2 spins in an external time-dependent magnetic field, considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos that can destroy the stability of quantum operations. The standard viewpoint is that the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a nonhomogeneous magnetic field can strongly reduce quantum chaos effects. We give analytical estimates that explain this effect, together with numerical data supporting our analysis.

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PubMed2001

One-dimensional quantum models with correlated disorder versus classical oscillators with colored noise.

We perform an analytical study of the correspondence between a classical oscillator with frequency perturbed by a colored noise and the one-dimensional Anderson-type model with weak correlated diagonal disorder. It is rigorously shown that localization of electronic states in the quantum model corresponds to exponential divergence of nearby trajectories of the classical random oscillator. We discuss the relation between the localization length for the quantum model and the rate of energy growth for the stochastic oscillator. Finally, we examine the problem of electron transmission through a finite disordered lattice by considering the evolution of the classical oscillator.

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PubMed2001

Delocalization border and onset of chaos in a model of quantum computation.

We study the properties of spectra and eigenfunctions for a chain of 1/2 spins (qubits) in an external time-dependent magnetic field and under the conditions of nonselective excitation (when the amplitude of the magnetic field is large). This model is known as a possible candidate for experimental realization of quantum computation. We present the theory for finding delocalization transitions and show that for the interaction between nearest qubits, the transition is very different from that in quantum chaos. We explain this phenomena by showing that in the considered region of parameters our model is close to an integrable one. According to a general opinion, the threshold for the onset of quantum chaos due to the interqubit interaction decreases with an increase of the number of qubits. Contrary to this expectation, for a magnetic field with constant gradient we have found that chaos border does not depend on the number of qubits. We give analytical estimates that explain this effect, together with numerical data supporting our analysis. Random models with long-range interactions have been studied as well. In particular, we show that in this case the delocalization and quantum chaos borders coincide.

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PubMed2001

Entropy production and wave packet dynamics in the Fock space of closed chaotic many-body systems.

Highly excited many-particle states in quantum systems such as nuclei, atoms, quantum dots, spin systems, quantum computers, etc., can be considered as "chaotic" superpositions of mean-field basis states (Slater determinants, products of spin or qubit states). This is due to a very high level density of many-body states that are easily mixed by a residual interaction between particles (quasiparticles). For such systems, we have derived simple analytical expressions for the time dependence of the energy width of wave packets, as well as for the entropy, number of principal basis components, and inverse participation ratio, and tested them in numerical experiments. It is shown that the energy width Delta(t) increases linearly and very quickly saturates. The entropy of a system increases quadratically, S(t) approximately t(2), at small times, and afterward can grow linearly, S(t) approximately t, before saturation. Correspondingly, the number of principal components determined by the entropy N(pc) approximately exp[S(t)] or by the inverse participation ratio increases exponentially fast before saturation. These results are explained in terms of a cascade model which describes the flow of excitation in the Fock space of basis components. Finally, the striking phenomenon of damped oscillations in the Fock space at the transition to equilibrium is discussed.

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PubMed2001

Periodic chaotic billiards: quantum-classical correspondence in energy space.

We investigate the properties of eigenstates and local density of states (LDOS) for a periodic two-dimensional rippled billiard, focusing on their quantum-classical correspondence in energy representation. To construct the classical counterparts of LDOS and the structure of eigenstates (SES), the effects of the boundary are first incorporated (via a canonical transformation) into an effective potential, rendering the one-particle motion in the 2D rippled billiard equivalent to that of two interacting particles in 1D geometry. We show that classical counterparts of SES and LDOS in the case of strong chaotic motion reveal quite a good correspondence with the quantum quantities. We also show that the main features of the SES and LDOS can be explained in terms of the underlying classical dynamics, in particular, of certain periodic orbits. On the other hand, statistical properties of eigenstates and LDOS turn out to be different from those prescribed by random matrix theory. We discuss the quantum effects responsible for the nonergodic character of the eigenstates and individual LDOS that seem to be generic for this type of billiards with a large number of transverse channels.

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PubMed2001

Unconventional decay law for excited states in closed many-body systems.

We study the time evolution of an initially excited many-body state in a finite system of interacting Fermi particles in the situation when the interaction gives rise to the "chaotic" structure of compound states. This situation is generic for highly excited many-particle states in quantum systems such as heavy nuclei, complex atoms, quantum dots, spin systems, and quantum computers. For a strong interaction the leading term for the return probability W(t) has the form W(t) approximately exp(-Delta(2)(E)t(2)) with Delta(2)(E) as the variance of the strength function. The conventional exponential linear dependence W(t)=C exp(-Gammat) formally arises for a very larger time. However, the prefactor C turns out to be exponentially large, thus resulting in a strong difference from the conventional estimate for W(t).

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