Nuclear structure, random interactions and mesoscopic physics

Zelevinsky, Vladimir; Volya, Alexander

doi:10.1016/j.physrep.2003.10.008

Cited by 80 publications

(49 citation statements)

References 97 publications

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“…The unexpected result is a clear predominance of ground states of total spin J = 0. Statistical considerations [37] qualitatively explain this by assuming that the wave functions are randomized and prefer maximal or minimal values of total spin (precursor of ferromagnetic or anti-ferromagnetic order). It is interesting that the observed effect seems to be different from the spin glass system [38], where the ground state spin on average grows as the square root of the number N p of interacting spins.…”

Section: Two-body Random Interactionmentioning

confidence: 99%

Quantum chaos and thermalization in isolated systems of interacting particles

et al. 2016

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This 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.

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Section: Two-body Random Interactionmentioning

confidence: 99%

Quantum chaos and thermalization in isolated systems of interacting particles

et al. 2016

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“…The SR state emerges with a very simple structure in the original basis (blue lines), having a very low entropy. The other states stay at the GOE predicted average value S = ln(0.48N) [3], which in this case is 3.2. We see that in the energy basis (black lines), where the Hamiltonian is diagonal for κ = 0, we have the complementary situation with entropy.…”

Section: Opening the System Energies And Entropymentioning

confidence: 79%

“…The basic structure of the model is a Hermitian Hamiltonian with coupling to the continuum modeled by the addition of an imaginary part or doorway state, see [1][2][3]. The energies of the original Hamiltonian acquire widths.…”

Section: Introductionmentioning

confidence: 99%

Open quantum systems and random matrix theory

Mulhall

2014

AIP Conference Proceedings

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A simple model for open quantum systems is analyzed with Random Matrix Theory. The system is coupled to the continuum in a minimal way. In this paper the effect of opening the system on the level statistics is seen. In particular the ∆ 3 (L) statistic, the width distribution and the level spacing are examined as a function of the strength of this coupling. The emergence of a superradiant transition is observed. The level spacing and ∆ 3 (L) statistic exhibit the signatures of missed levels or intruder levels as the super-radiant state is formed. * Electronic address: mulhalld2@scranton.edu

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“…The J0D for 6 particles interacting on a j = 19/2 level was found to be due to the widths of the distributions of E J . The problem of N fermions on a single j level was treated as a gas of fermions and a statistical treatment led to some closed form results for the yrast lines, the distribution of J gs and many more observables [21,22]. A key step in that analysis was the assumption of geometric chaoticity, the idea that many couplings of angular momentum proceed like a random walk.…”

Section: Explanationsmentioning

confidence: 99%

Randomly interacting bosons on two spin levels

Mulhall¹

2017

AIP Conference Proceedings

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Abstract. The problem of random interactions leading to regular spectra in shell model type simulations is described. The key results are reviewed alnog with a selection of the explanations. A model system of N particles on 2 spin levels having random 2-body collisions that conserve angular momentum is examined. Preliminary results are described, including the ground state spin distributions peaked at extreme values of angular momentum, signatures of rotational bands, and smooth parabolic yrast lines. A simple random matrix theory analysis shows signatures of quantum chaos in the level spacing distribution and the ∆ 3 statistic.

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Nuclear structure, random interactions and mesoscopic physics

Cited by 80 publications

References 97 publications

Quantum chaos and thermalization in isolated systems of interacting particles

Quantum chaos and thermalization in isolated systems of interacting particles

Open quantum systems and random matrix theory

Randomly interacting bosons on two spin levels

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