scholarly journals Probing Many-Body Systems Near Spectral Degeneracies

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1796
Author(s):  
Klaus Ziegler
Keyword(s):  
Decay Rate ◽  
Correlation Matrix ◽  
Time Correlation ◽  
General Concept ◽  
Quantum Systems ◽  
Quantum Evolution ◽  
Many Body ◽  
Space Localization ◽  
Many Body Systems ◽  
Random Times

The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially decaying part. This separation is strongly affected when spectral degeneracies occur, for instance, in the presence of spontaneous symmetry breaking. Moreover, the slowest decay rate is determined by the smallest energy level spacing, and this decay rate diverges at the spectral degeneracies. Probing the quantum evolution with the diagonal elements of the time correlation matrix is discussed as a general concept and tested in the case of a bosonic Josephson junction. It reveals for the latter characteristic properties at the transition to Hilbert-space localization.

scholarly journals QUANTUM DYNAMICS WITH AN ENSEMBLE OF HAMILTONIANS

2013 ◽  
Vol 27 (26) ◽  
pp. 1330019 ◽  
Author(s):  
ARMIN RAHMANI
Keyword(s):  
Disordered Systems ◽  
Quantum Dynamics ◽  
Nonequilibrium Dynamics ◽  
Quantum Evolution ◽  
Many Body ◽  
Driven Systems ◽  
Shortcuts To Adiabaticity ◽  
New Directions ◽  
Time Quantum ◽  
Many Body Systems

We review recent progress in the nonequilibrium dynamics of thermally isolated many-body quantum systems, evolving with an ensemble of Hamiltonians as opposed to deterministic evolution with a single time-dependent Hamiltonian. Such questions arise in (i) quantum dynamics of disordered systems, where different realizations of disorder give rise to an ensemble of real-time quantum evolutions, (ii) quantum evolution with noisy Hamiltonians (temporal disorder), which leads to stochastic Schrödinger equations, and, (iii) in the broader context of quantum optimal control, where one needs to analyze an ensemble of permissible protocols in order to find one that optimizes a given figure of merit. The theme of ensemble quantum evolution appears in several emerging new directions in noneqilibrium quantum dynamics of thermally isolated many-body systems, which include many-body localization, noise-driven systems, and shortcuts to adiabaticity.

scholarly journals Experimental Test of Spontaneous Correlation and Anomalous Sensitivity in Finite Highly Excited Many-Body Systems

2003 ◽  
Vol 12 (03) ◽  
pp. 377-393 ◽  
Author(s):  
Qi Wang ◽  
Sergey Yu Kun ◽  
Wendong Tian ◽  
Songlin Li ◽  
Zhonghe Jiang ◽  
...  
Keyword(s):  
Cross Sections ◽  
Experimental Test ◽  
Heavy Ion ◽  
Quantum Systems ◽  
Slow Phase ◽  
Many Body ◽  
Ion Collisions ◽  
Excited Complex ◽  
Many Body Systems ◽  
Phase Randomization

We have tested recent suggestion of anomalous sensitivity in highly excited quantum many-body systems. Two independent measurements of cross sections for the 19 F + 93 Nb strongly dissipative heavy-ion collisions have been performed at incident energies from 102 to 108 MeV in steps of 250 keV. In the two measurements we used different, independently prepared, 93Nb target foils with nominally the same thickness. The data indicate statistically significant non-reproducibility of the energy oscillating yields in the two measurements. The observed non-reproducibility is consistent with recent theoretical arguments on spontaneous correlation, slow phase randomization and chaos in highly excited complex quantum systems.

scholarly journals Randomness of Eigenstates of Many-Body Quantum Systems

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 227 ◽  
Author(s):  
Li-Zhen Sun ◽  
Qingmiao Nie ◽  
Haibin Li
Keyword(s):  
Hard Core ◽  
Underlying Mechanism ◽  
Quantum Systems ◽  
One Dimension ◽  
Many Body ◽  
Random Vectors ◽  
Boson System ◽  
Many Body Systems

The emergence of random eigenstates of quantum many-body systems in integrable-chaos transitions is the underlying mechanism of thermalization for these quantum systems. We use fidelity and modulus fidelity to measure the randomness of eigenstates in quantum many-body systems. Analytic results of modulus fidelity between random vectors are obtained to be a judge for the degree of randomness. Unlike fidelity, which just refers to a kind of criterion of necessity, modulus fidelity can measure the degree of randomness in eigenstates of a one-dimension (1D) hard-core boson system and identifies the integrable-chaos transition in this system.

scholarly journals Order Indices and Entanglement Production in Quantum Systems

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 565 ◽  
Author(s):  
Vyacheslav I. Yukalov
Keyword(s):  
Long Range ◽  
Short Range ◽  
Quantum Systems ◽  
Quantum Operation ◽  
Many Body ◽  
Finite Systems ◽  
Production Order ◽  
Intimate Relation ◽  
Many Body Systems ◽  
Statistical Systems

The review is devoted to two important quantities characterizing many-body systems, order indices and the measure of entanglement production. Order indices describe the type of order distinguishing statistical systems. Contrary to the order parameters characterizing systems in the thermodynamic limit and describing long-range order, the order indices are applicable to finite systems and classify all types of orders, including long-range, mid-range, and short-range orders. The measure of entanglement production quantifies the amount of entanglement produced in a many-partite system by a quantum operation. Despite that the notions of order indices and entanglement production seem to be quite different, there is an intimate relation between them, which is emphasized in the review.

REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

2008 ◽  
Vol 17 (supp01) ◽  
pp. 304-317
Author(s):  
Y. M. ZHAO
Keyword(s):  
Ground State ◽  
Collective Motion ◽  
Regular Structure ◽  
Positive Parity ◽  
Many Body ◽  
Random Interactions ◽  
Atomic Nuclei ◽  
Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

scholarly journals Emergence of a Renormalized 1/N Expansion in Quenched Critical Many-Body Systems

2021 ◽  
Vol 126 (11) ◽  
Author(s):  
Benjamin Geiger ◽  
Juan Diego Urbina ◽  
Klaus Richter
Keyword(s):  
Many Body ◽  
Many Body Systems

scholarly journals Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems

2020 ◽  
Vol 125 (26) ◽  
Author(s):  
Norifumi Matsumoto ◽  
Kohei Kawabata ◽  
Yuto Ashida ◽  
Shunsuke Furukawa ◽  
Masahito Ueda
Keyword(s):  
Phase Transition ◽  
Continuous Phase ◽  
Many Body ◽  
Continuous Phase Transition ◽  
Many Body Systems ◽  
Gap Closing

scholarly journals Universal relations for ultracold reactive molecules

2020 ◽  
Vol 6 (51) ◽  
pp. eabd4699
Author(s):  
Mingyuan He ◽  
Chenwei Lv ◽  
Hai-Qing Lin ◽  
Qi Zhou
Keyword(s):  
Critical Role ◽  
Interaction Strength ◽  
Quantum Correlations ◽  
Polar Molecules ◽  
Many Body ◽  
Density Correlation ◽  
Ultracold Polar Molecules ◽  
Unexplored Area ◽  
Many Body Systems

The realization of ultracold polar molecules in laboratories has pushed physics and chemistry to new realms. In particular, these polar molecules offer scientists unprecedented opportunities to explore chemical reactions in the ultracold regime where quantum effects become profound. However, a key question about how two-body losses depend on quantum correlations in interacting many-body systems remains open so far. Here, we present a number of universal relations that directly connect two-body losses to other physical observables, including the momentum distribution and density correlation functions. These relations, which are valid for arbitrary microscopic parameters, such as the particle number, the temperature, and the interaction strength, unfold the critical role of contacts, a fundamental quantity of dilute quantum systems, in determining the reaction rate of quantum reactive molecules in a many-body environment. Our work opens the door to an unexplored area intertwining quantum chemistry; atomic, molecular, and optical physics; and condensed matter physics.

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