scholarly journals Non-thermal fixed points: Universal dynamics far from equilibrium

2019 ◽  
Vol 34 (29) ◽  
pp. 1941006 ◽  
Author(s):  
Christian-Marcel Schmied ◽  
Aleksandr N. Mikheev ◽  
Thomas Gasenzer
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Turbulent Transport ◽  
Topological Defects ◽  
Effective Field ◽  
Integral Approach ◽  
Many Body ◽  
Universal Scaling ◽  
Many Body Systems

In this article we give an overview of the concept of universal dynamics near non-thermal fixed points in isolated quantum many-body systems. We outline a non-perturbative kinetic theory derived within a Schwinger–Keldysh closed-time path-integral approach, as well as a low-energy effective field theory which enable us to predict the universal scaling exponents characterizing the time evolution at the fixed point. We discuss the role of wave-turbulent transport in the context of such fixed points and discuss universal scaling evolution of systems bearing ensembles of (quasi) topological defects. This is rounded off by the recently introduced concept of prescaling as a generic feature of the evolution towards a non-thermal fixed point.

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.

Coarse-Graining, Scaling, and Hierarchies

2004 ◽  
Author(s):  
Juan Pérez-Mercade
Keyword(s):  
Differential Equations ◽  
Fixed Points ◽  
Correlation Functions ◽  
Nonlinear Partial Differential Equations ◽  
Coarse Graining ◽  
Power Laws ◽  
Effective Parameters ◽  
Many Body ◽  
Anomalous Dimensions ◽  
Many Body Systems

We present a scenario that is useful for describing hierarchies within classes of many-component systems. Although this scenario may be quite general, it will be illustrated in the case of many-body systems whose space-time evolution can be described by a class of stochastic parabolic nonlinear partial differential equations. The stochastic component we will consider is in the form of additive noise, but other forms of noise such as multiplicative noise may also be incorporated. It will turn out that hierarchical behavior is only one of a class of asymptotic behaviors that can emerge when an out-of-equilibrium system is coarse grained. This phenomenology can be analyzed and described using the renormalization group (RG) [6, 15]. It corresponds to the existence of complex fixed points for the parameters characterizing the system. As is well known (see, for example, Hochberg and Perez-Mercader [8] and Onuki [12] and the references cited there), parameters such as viscosities, noise couplings, and masses evolve with scale. In other words, their values depend on the scale of resolution at which the system is observed (examined). These scaledependent parameters are called effective parameters. The evolutionary changes due to coarse graining or, equivalently, changes in system size, are analyzed using the RG and translate into differential equations for the probability distribution function [8] of the many-body system, or the n-point correlation functions and the effective parameters. Under certain conditions and for systems away from equilibrium, some of the fixed points of the equations describing the scale dependence of the effective parameters can be complex; this translates into complex anomalous dimensions for the stochastic fields and, therefore, the correlation functions of the field develop a complex piece. We will see that basic requirements such as reality of probabilities and maximal correlation lead, in the case of complex fixed points, to hierarchical behavior. This is a first step for the generalization of extensive behavior as described by real power laws to the case of complex exponents and the study of hierarchical behavior.

scholarly journals F-Metric, F-Contraction and Common Fixed-Point Theorems with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 586 ◽  
Author(s):  
Awais Asif ◽  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Third ◽  
Set Valued Mappings ◽  
Common Fixed Point Theorems

In this paper, we noticed that the existence of fixed points of F-contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

scholarly journals On the widths and binding energies of K− nuclear states and the role of K− multi-nucleon interactions

2018 ◽  
Vol 181 ◽  
pp. 01009
Author(s):  
Jaroslava Hrtankova ◽  
Jiří Mareš
Keyword(s):  
Bound States ◽  
Binding Energies ◽  
Many Body ◽  
Nucleon Interaction ◽  
Substantial Impact ◽  
Coupled Channels ◽  
Self Consistent ◽  
Interaction Term ◽  
Many Body Systems

We report on our recent self-consistent calculations of K− nuclear quasi-bound states using K− optical potentials derived from chirally motivated meson-baryon coupled channels models [1, 2]. The K− single-nucleon potentials were supplemented by a phenomenological K− multi-nucleon interaction term introduced to achieve good fits to K− atom data. We demonstrate a substantial impact of the K− multi-nucleon absorption on the widths of K− nuclear states. If such states ever exist in nuclear many-body systems, their widths are excessively large to allow observation.

PHASE DIAGRAMS OF VARIOUS KINDS OF ISING SPIN-GLASS MODELS WITH A NEW PARAMETER TO CONTROL FRUSTRATION ON A GIVEN LATTICE

2010 ◽  
Vol 24 (05) ◽  
pp. 567-573 ◽  
Author(s):  
YOUICHIRO HASHIZUME ◽  
XIAO HU ◽  
MASUO SUZUKI
Keyword(s):  
Phase Diagram ◽  
Spin Glass ◽  
Effective Field ◽  
Continuous Control ◽  
Continuous Change ◽  
Many Body ◽  
Ising Spin ◽  
Spin Interactions ◽  
Transition Points

In this study, we introduce a new method to control continuously the frustration caused by the quenched interaction in a given lattice, and we examine how the phenomenon changes by continuous control of the frustration, especially examining a continuous change of phase transition points. For this purpose, we introduce many-body correlation among original spin-interactions using a distribution function to express the correlations, which plays a role of a parameter to control the frustration. The transition points have been obtained by the cluster effective field theory. As a result, an interesting phase diagram has been obtained for the continuous change of frustration. Furthermore, phase transitions of various models can be analyzed systematically in a fixed lattice from this phase diagram with a variable of continuous change of frustration. In addition, it is understood that the spin-glass transition points do not depend on the disorder of the interaction and are decided only by the frustration.

scholarly journals Two- and three-body contacts in the unitary Bose gas

Science ◽  
2017 ◽  
Vol 355 (6323) ◽  
pp. 377-380 ◽  
Author(s):  
Richard J. Fletcher ◽  
Raphael Lopes ◽  
Jay Man ◽  
Nir Navon ◽  
Robert P. Smith ◽  
...  
Keyword(s):  
Bose Gas ◽  
Many Body ◽  
Body Contact ◽  
Wide Range ◽  
Pairwise Correlations ◽  
Efimov Physics ◽  
Many Body Systems ◽  
Three Body ◽  
Profound Insight

In many-body systems governed by pairwise contact interactions, a wide range of observables is linked by a single parameter, the two-body contact, which quantifies two-particle correlations. This profound insight has transformed our understanding of strongly interacting Fermi gases. Using Ramsey interferometry, we studied coherent evolution of the resonantly interacting Bose gas, and we show here that it cannot be explained by only pairwise correlations. Our experiments reveal the crucial role of three-body correlations arising from Efimov physics and provide a direct measurement of the associated three-body contact.

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