Unconventional critical behaviour in quantum systems with interactions decaying as a power law

1994 ◽  
Vol 205 (4) ◽  
pp. 718-737
Author(s):  
A.Caramico D'Auria ◽  
L. De Cesare ◽  
I. Rabuffo
Keyword(s):  
Power Law ◽  
Quantum Systems ◽  
Critical Behaviour

scholarly journals Intermittency of storms and substorms: is it related to the critical behaviour?

2009 ◽  
Vol 27 (5) ◽  
pp. 2011-2018 ◽  
Author(s):  
P. Dobias ◽  
J. A. Wanliss
Keyword(s):  
Power Law ◽  
Normal State ◽  
Fano Factor ◽  
Critical Behaviour ◽  
Critical Systems ◽  
Dynamical Processes ◽  
Storms And Substorms ◽  
The Relationship

Abstract. Intermittency is one of the possible means of quantifying dynamics of fractal processes. In this paper, the analysis of the intermittency of magnetospheric storms and substorms is presented. The analysis allows for a classification of the processes in terms of the power-law scaling of the magnitude of deviations of the index values from the values at quiet times (normal state), and the relative timings of occurrences of such deviations. These are expressed in terms of the co-dimension and the Fano factor. The relationship between the two is related to the nature of the processes behind the observed storm and substorm dynamics. The results suggest that there is a similarity between the two, and therefore it is possible that there are common dynamical processes behind the storms and substorms. In particular, it appears that both of them behave consistently with what would be expected for critical systems, which is consistent with the conclusions of several previous works.

scholarly journals Quantum Maps with Memory from Generalized Lindblad Equation

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 544
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Discrete Time ◽  
Power Law ◽  
Quantum Dynamics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Periodic Sequence ◽  
Lindblad Equation ◽  
Open Quantum ◽  
Systems With Memory ◽  
With Memory

In this paper, we proposed the exactly solvable model of non-Markovian dynamics of open quantum systems. This model describes open quantum systems with memory and periodic sequence of kicks by environment. To describe these systems, the Lindblad equation for quantum observable is generalized by taking into account power-law fading memory. Dynamics of open quantum systems with power-law memory are considered. The proposed generalized Lindblad equations describe non-Markovian quantum dynamics. The quantum dynamics with power-law memory are described by using integrations and differentiation of non-integer orders, as well as fractional calculus. An example of a quantum oscillator with linear friction and power-law memory is considered. In this paper, discrete-time quantum maps with memory, which are derived from generalized Lindblad equations without any approximations, are suggested. These maps exactly correspond to the generalized Lindblad equations, which are fractional differential equations with the Caputo derivatives of non-integer orders and periodic sequence of kicks that are represented by the Dirac delta-functions. The solution of these equations for coordinates and momenta are derived. The solutions of the generalized Lindblad equations for coordinate and momentum operators are obtained for open quantum systems with memory and kicks. Using these solutions, linear and nonlinear quantum discrete-time maps are derived.

scholarly journals HIDDEN UNITY IN THE QUANTUM DESCRIPTION OF MATTER

2003 ◽  
Vol 17 (28) ◽  
pp. 5413-5423 ◽  
Author(s):  
G. ORTIZ ◽  
C. D. BATISTA
Keyword(s):  
General Concept ◽  
Quantum Systems ◽  
Fundamental Concept ◽  
Critical Behaviour ◽  
Broken Symmetry ◽  
Quantum Description ◽  
Algebraic Framework ◽  
Complex Phenomena ◽  
Physical Phenomena

We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterised by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity behind seemingly unrelated physical phenomena, thus establishing exact connections between them. This leads to the fundamental concept of universality of physical phenomena, a general concept not restricted to the domain of critical behaviour. Key to our framework is the concept of languages and the construction of dictionaries relating them.

Critical behaviour of quantum systems with quenched point impurities

1984 ◽  
Vol 106 (4) ◽  
pp. 175-178 ◽  
Author(s):  
E.R. Korutcheva ◽  
D.I. Uzunov
Keyword(s):  
Quantum Systems ◽  
Critical Behaviour

Critical Behaviour of the Heat Capacity Near the α-β Phase Transition in Quartz

2013 ◽  
Vol 32 (2) ◽  
pp. 189-194 ◽  
Author(s):  
H. Yurtseven ◽  
M. Desticioğlu
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Critical Exponent ◽  
Power Law ◽  
Theoretical Models ◽  
Order Transition ◽  
Critical Behaviour ◽  
Experimental Heat ◽  
Β Phase ◽  
Second Order Transition

AbstractThe α-β transition (TQ = 578°C) is studied in quartz by analyzing the experimental heat capacity Cp data taken from the literature, using a power-law formula. Values of the critical exponent α for Cp are extracted below and above TQ, which describe the α-β transition as a second order transition in quartz. The α values obtained here are compared with the predictions of the theoretical models.

Sign in / Sign up

Export Citation Format

Share Document