214 research outputs found
Bar-invariant bases of the quantum cluster algebra of type
No full textsummary:We construct bar-invariant -bases of the quantum cluster algebra of the valued quiver , one of which coincides with the quantum analogue of the basis of the corresponding cluster algebra discussed in P. Sherman, A. Zelevinsky: Positivity and canonical bases in rank 2 cluster algebras of finite and affine types, Moscow Math. J., 4, 2004, 947–974
Distribution of Resonance Widths and Dynamics of Continuum Coupling
No full textWe analyze the statistics of resonance widths in a many-body Fermi system with open decay channels. Depending on the strength of continuum coupling, such a system reveals growing deviations from the standard chi-square (Porter-Thomas) width distribution. The deviations emerge from the process of increasing interaction of intrinsic states through common decay channels; in the limit of perfect coupling this process leads to the superradiance phase transition. The width distribution depends also on the intrinsic dynamics (chaotic versus regular). The results presented here are important for understanding the recent experimental data concerning the width distribution for neutron resonances in nuclei
Diophantine non-integrability of a third order recurrence with the Laurent property
No full textWe consider a one-parameter family of third order nonlinear recurrence relations. Each member of this family satisfies the singularity confinement test, has a conserved quantity, and moreover has the Laurent property: all of the iterates are Laurent polynomials in the initial data. However, we show that these recurrences are not Diophantine integrable according to the definition proposed by Halburd. Explicit bounds on the asymptotic growth of the heights of iterates are obtained for a special choice of initial data. As a by-product of our analysis, infinitely many solutions are found for a certain family of Diophantine equations, studied by Mordell, that includes Markoff's equation
Transport through nanostructures with asymmetric coupling to the leads
No full textUsing an approach to open quantum systems based on the effective non-Hermitian Hamiltonian, we fully describe transport properties for a paradigmatic model of a coherent quantum transmitter: a finite sequence of square potential barriers. We consider the general case of asymmetric external barriers and variable coupling strength to the environment. We demonstrate that transport properties are very sensitive to the degree of opening of the system and determine the parameters for maximum transmission at any given degree of asymmetry. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian, we show a double transition to a super-radiant regime where the transport properties and the structure of resonances undergo a strong change. We extend our analysis to the presence of disorder and to higher dimensions
Internal chaos in an open quantum system: From Ericson to conductance fluctuations
No full textThe model of an open Fermi system is used for studying the interplay of intrinsic chaos and irreversible decay into open continuum channels. Two versions of the model are characterized by one-body chaos coming from disorder or by many-body chaos due to the inter-particle interactions. The continuum coupling is described by the effective non-Hermitian Hamiltonian. Our main interest is in specific correlations of cross-sections for various channels in dependence on the coupling strength and degree of internal chaos. The results are generic and refer to common features of various mesoscopic objects including conductance fluctuations and resonance nuclear reactions
Quantum chaos and thermalization in isolated systems of interacting particles
No full textThis review is devoted to the problem of thermalization in a small isolated conglomerate
of interacting constituents. A variety of physically important systems of intensive
current interest belong to this category: complex atoms, molecules (including biological
molecules), nuclei, small devices of condensed matter and quantum optics on nano-
and micro-scale, cold atoms in optical lattices, ion traps. Physical implementations of
quantum computers, where there are many interacting qubits, also fall into this group.
Statistical regularities come into play through inter-particle interactions, which have two
fundamental components: mean field, that along with external conditions, forms the
regular component of the dynamics, and residual interactions responsible for the complex
structure of the actual stationary states. At sufficiently high level density, the stationary
states become exceedingly complicated superpositions of simple quasiparticle excitations.
At this stage, regularities typical of quantum chaos emerge and bring in signatures of
thermalization. We describe all the stages and the results of the processes leading to
thermalization, using analytical and massive numerical examples for realistic atomic,
nuclear, and spin systems, as well as for models with random parameters. The structure
of stationary states, strength functions of simple configurations, and concepts of entropy
and temperature in application to isolated mesoscopic systems are discussed in detail. We
conclude with a schematic discussion of the time evolution of such systems to equilibrium
Atomic Nucleus as Chaotic Quantum Many-Body System
No full textQuantum many-body chaos is described as a practical (theoretical, experimental, and computational) instru-ment in physics of mesoscopic systems of interacting particles. Using mainly nuclear physics applications, it is shown that interactions of constituents create stationary states of high complexity with respect to the nean-field basis with observable properties smoothly changing along the spectrum. Both local Gaussian orthogonal ensemble type features and the global evolution along the spectrum are used to understand the many-body physics and define thermodynamic properties of isolated mesoscopic objects. Among the examples discussed, especially interesting is a chaotic enhancement of weak perturbations illustrated by a large parity violation in neutron resonances on heavy nuclei. Artificially introduced chaotic elements are used to explore the nuclear landscape and predict phase transformations
Cooper pair correlations and energetic knock-out reactions
No full textTwo-nucleon removal (or knock-out) reactions at intermediate energies are a developing tool for both nuclear spectroscopy and for the study of certain nucleon correlations in very exotic and some stable nuclei. We present an overview of these reactions with specific emphasis on the nature of the two-nucleon correlations that can be probed. We outline future possibilities and tests needed to fully establish these sensitivities
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