IV. ComputationalMetho ds for the Simulation of Classical and Quantum Many Body Systems Arising from Nonextensive Thermostatistics

2007 ◽  
pp. 193-233 ◽  
Author(s):  
I. Andricioaei ◽  
J.E. Straub
Keyword(s):  
Many Body ◽  
Many Body Systems

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.

scholarly journals Epidemic growth and Griffiths effects on an emergent network of excited atoms

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
T. M. Wintermantel ◽  
M. Buchhold ◽  
S. Shevate ◽  
M. Morgado ◽  
Y. Wang ◽  
...  
Keyword(s):  
Complex Systems ◽  
Power Laws ◽  
Excitation Density ◽  
Griffiths Phase ◽  
Many Body ◽  
Excited Atoms ◽  
Equilibrium Dynamics ◽  
Many Body Systems ◽  
Excitation Number ◽  
Non Equilibrium

AbstractWhether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report a striking correspondence between the excitation dynamics of a laser driven gas of Rydberg atoms and the spreading of diseases, which in turn opens up a controllable platform for studying non-equilibrium dynamics on complex networks. The competition between facilitated excitation and spontaneous decay results in sub-exponential growth of the excitation number, which is empirically observed in real epidemics. Based on this we develop a quantitative microscopic susceptible-infected-susceptible model which links the growth and final excitation density to the dynamics of an emergent heterogeneous network and rare active region effects associated to an extended Griffiths phase. This provides physical insights into the nature of non-equilibrium criticality in driven many-body systems and the mechanisms leading to non-universal power-laws in the dynamics of complex systems.

scholarly journals Probing phase transitions of holographic entanglement entropy with fixed area states

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Donald Marolf ◽  
Shannon Wang ◽  
Zhencheng Wang
Keyword(s):  
Phase Transitions ◽  
Entanglement Entropy ◽  
Many Body ◽  
Btz Black Hole ◽  
Holographic Entanglement Entropy ◽  
Volume Limit ◽  
Cutoff Dependence ◽  
Diagonal Approximation ◽  
Fixed Area ◽  
Many Body Systems

Abstract Recent results suggest that new corrections to holographic entanglement entropy should arise near phase transitions of the associated Ryu-Takayanagi (RT) surface. We study such corrections by decomposing the bulk state into fixed-area states and conjecturing that a certain ‘diagonal approximation’ will hold. In terms of the bulk Newton constant G, this yields a correction of order O(G−1/2) near such transitions, which is in particular larger than generic corrections from the entanglement of bulk quantum fields. However, the correction becomes exponentially suppressed away from the transition. The net effect is to make the entanglement a smooth function of all parameters, turning the RT ‘phase transition’ into a crossover already at this level of analysis.We illustrate this effect with explicit calculations (again assuming our diagonal approximation) for boundary regions given by a pair of disconnected intervals on the boundary of the AdS3 vacuum and for a single interval on the boundary of the BTZ black hole. In a natural large-volume limit where our diagonal approximation clearly holds, this second example verifies that our results agree with general predictions made by Murthy and Srednicki in the context of chaotic many-body systems. As a further check on our conjectured diagonal approximation, we show that it also reproduces the O(G−1/2) correction found Penington et al. for an analogous quantum RT transition. Our explicit computations also illustrate the cutoff-dependence of fluctuations in RT-areas.

scholarly journals Undecidability in quantum thermalization

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Naoto Shiraishi ◽  
Keiji Matsumoto
Keyword(s):  
Turing Machine ◽  
Thermal Equilibrium ◽  
General Theorem ◽  
Nearest Neighbour ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Universal Turing Machine ◽  
Many Body Systems ◽  
Neighbour Interaction

AbstractThe investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.

scholarly journals Ultrafast dynamical Lifshitz transition

2021 ◽  
Vol 7 (17) ◽  
pp. eabd9275
Author(s):  
Samuel Beaulieu ◽  
Shuo Dong ◽  
Nicolas Tancogne-Dejean ◽  
Maciej Dendzik ◽  
Tommaso Pincelli ◽  
...  
Keyword(s):  
Fermi Surface ◽  
Colossal Magnetoresistance ◽  
Surface Topology ◽  
Strongly Correlated ◽  
Many Body ◽  
Time Resolved ◽  
Weyl Semimetal ◽  
Lifshitz Transition ◽  
Fermi Surface Topology ◽  
Many Body Systems

Fermi surface is at the heart of our understanding of metals and strongly correlated many-body systems. An abrupt change in the Fermi surface topology, also called Lifshitz transition, can lead to the emergence of fascinating phenomena like colossal magnetoresistance and superconductivity. While Lifshitz transitions have been demonstrated for a broad range of materials by equilibrium tuning of macroscopic parameters such as strain, doping, pressure, and temperature, a nonequilibrium dynamical route toward ultrafast modification of the Fermi surface topology has not been experimentally demonstrated. Combining time-resolved multidimensional photoemission spectroscopy with state-of-the-art TDDFT+U simulations, we introduce a scheme for driving an ultrafast Lifshitz transition in the correlated type-II Weyl semimetal Td-MoTe2. We demonstrate that this nonequilibrium topological electronic transition finds its microscopic origin in the dynamical modification of the effective electronic correlations. These results shed light on a previously unexplored ultrafast scheme for controlling the Fermi surface topology in correlated quantum materials.

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

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