scholarly journals Interplay of symmetry and topology in science

2014 ◽  
Vol 70 (a1) ◽  
pp. C1419-C1419
Author(s):  
Boris Zhilinskii
Keyword(s):  
Classical System ◽  
Quantum Systems ◽  
Qualitative Theory ◽  
Topological Invariant ◽  
Particle Systems ◽  
Qualitative Description ◽  
Energy Bands ◽  
And Topology ◽  
Finite Particle

Qualitative methods in natural science are based mainly on simultaneous use of symmetry and topology arguments. The idea of the present talk is to demonstrate how the corresponding mathematical tools (based on symmetry and topology arguments) initially applied to describe classification of different phases of matter and transitions between them are extended to construct qualitative theory of finite particle systems and more general dynamical systems. I start with reminding basic notions and tools associated with application of group action ideas to physics as initiated and developed by Louis Michel (1923-1999) [1,2]. Then geometric combinatorial and topological ideas are used to give qualitative description of singularities of dynamical integrable classical system and their quantum analogs. Quantum monodromy and its various generalizations as well as description of energy bands of isolated finite particle quantum systems in terms of topological invariant, Chern number [3], will be discussed on concrete molecular and atomic examples.

Decoherence, Classical Properties and Entanglement of Quantum Systems

2001 ◽  
Vol 56 (1-2) ◽  
pp. 124-127
Author(s):  
Ph. Blanchard ◽  
R. Olkiewicz
Keyword(s):  
Environmental Monitoring ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum ◽  
Pure States

AbstractWe discuss the properties of decoherence and its role in the appearance of classical properties in open quantum systems. In particular, it is used for classification of pure states with respect to their ability to persist despite the environmental monitoring.

scholarly journals Extracting topological information from momentum space propagators

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Fabrizio Canfora ◽  
David Dudal ◽  
Alex Giacomini ◽  
Igor F. Justo ◽  
Pablo Pais ◽  
...  
Keyword(s):  
Gauge Invariance ◽  
Momentum Space ◽  
Chiral Symmetry Breaking ◽  
Topological Invariant ◽  
Analytic Structure ◽  
Topological Information ◽  
Gauge Transformations ◽  
Small Gauge ◽  
Topological Number

Abstract A new topological invariant quantity, sensitive to the analytic structure of both fermionic and bosonic propagators, is proposed. The gauge invariance of our construct is guaranteed for at least small gauge transformations. A generalization compatible with the presence of complex poles is introduced and applied to the classification of propagators typically emerging from non-perturbative considerations. We present partial evidence that the topological number can be used to detect chiral symmetry breaking or deconfinement.

Types of evidence used in Canadian provincial sport organisations

2019 ◽  
Vol 14 (2) ◽  
pp. 162-168 ◽  
Author(s):  
Kurtis Pankow ◽  
Katherine A Tamminen ◽  
Martin Camiré ◽  
Dany J MacDonald ◽  
Leisha Strachan ◽  
...  
Keyword(s):  
Decision Making ◽  
Thematic Analysis ◽  
Analysis Procedure ◽  
Qualitative Description ◽  
Sport Science ◽  
Different Types ◽  
Sport Organisation

Different types of evidence can be used to inform organisational decision making. The purpose of this study was to identify types of evidence used in sport organisations. Data were collected via interviews with 60 Canadian Provincial Sport Organisation representatives from five provinces. A qualitative description approach was used and data were subjected to an inductive-to-deductive thematic analysis procedure, with the deductive component guided by a classification of evidence types. Results demonstrated that knowledge and information (reported by 38 participants) and ideas and interests (28 participants) were the most frequently reported evidence types, whereas research (12 participants), political (2 participants), and economic (12 participants) evidence types were least frequently reported. These findings suggest that sport science researchers could communicate in the form of, and through mediums dedicated to, knowledge and information and ideas and interests in order to reach sport organisations.

A coupling of finite particle systems

1993 ◽  
Vol 30 (01) ◽  
pp. 258-262 ◽  
Author(s):  
T. S. Mountford
Keyword(s):  
Invariant Measure ◽  
Branching Process ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Initial Configuration ◽  
Limit Measure ◽  
One Dimensional ◽  
Interacting Particle ◽  
The One ◽  
Finite Particle

We show that for a large class of one-dimensional interacting particle systems, with a finite initial configuration, any limit measure , for a sequence of times tending to infinity, must be invariant. This result is used to show that the one-dimensional biased annihilating branching process with parameter > 1/3 converges in distribution to the upper invariant measure provided its initial configuration is almost surely finite and non-null.

scholarly journals Topology and Broken Symmetry in Floquet Systems

2020 ◽  
Vol 11 (1) ◽  
pp. 345-368 ◽  
Author(s):  
Fenner Harper ◽  
Rahul Roy ◽  
Mark S. Rudner ◽  
S.L. Sondhi
Keyword(s):  
Prima Facie ◽  
Particle Systems ◽  
Many Body ◽  
Nontrivial Behavior ◽  
Interacting Systems ◽  
State Of Affairs ◽  
Main Ideas ◽  
Nontrivial Topology ◽  
Infinite Temperature

Floquet systems are governed by periodic, time-dependent Hamiltonians. Prima facie they should absorb energy from the external drives involved in modulating their couplings and heat up to infinite temperature. However, this unhappy state of affairs can be avoided in many ways. Instead, as has become clear from much recent work, Floquet systems can exhibit a variety of nontrivial behavior—some of which is impossible in undriven systems. In this review, we describe the main ideas and themes of this work: novel Floquet drives that exhibit nontrivial topology in single-particle systems, the existence and classification of exotic Floquet drives in interacting systems, and the attendant notion of many-body Floquet phases and arguments for their stability to heating.

scholarly journals Koopman wavefunctions and classical–quantum correlation dynamics

2019 ◽  
Vol 475 (2229) ◽  
pp. 20180879 ◽  
Author(s):  
Denys I. Bondar ◽  
François Gay-Balmaz ◽  
Cesare Tronci
Keyword(s):  
Hamiltonian Structure ◽  
Classical System ◽  
Solvable Model ◽  
Infinite Family ◽  
Dynamical Theory ◽  
Quantum Systems ◽  
Von Neumann ◽  
Proposed Model ◽  
Exactly Solvable ◽  
Classical Quantum

Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman–von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical–quantum coupling. The proposed model not only describes the influence of a classical system onto a quantum one, but also the reverse effect—the quantum backreaction. These interactions are described by a new Hamiltonian wave equation overcoming shortcomings of currently employed models. For example, the density matrix of the quantum subsystem is always positive definite. While the Liouville density of the classical subsystem is generally allowed to be unsigned, its sign is shown to be preserved in time for a specific infinite family of hybrid classical–quantum systems. The proposed description is illustrated and compared with previous theories using the exactly solvable model of a degenerate two-level quantum system coupled to a classical harmonic oscillator.

scholarly journals A Supersymmetric Hierarchical Model for Weakly Disordered 3d Semimetals

2020 ◽  
Vol 21 (11) ◽  
pp. 3499-3574
Author(s):  
Giovanni Antinucci ◽  
Luca Fresta ◽  
Marcello Porta
Keyword(s):  
Multiscale Analysis ◽  
Three Dimensional ◽  
Quantum Systems ◽  
Supersymmetric Model ◽  
Energy Bands ◽  
Algebraic Decay ◽  
Group Methods ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Renormalization Group Methods

Abstract In this paper, we study a hierarchical supersymmetric model for a class of gapless, three-dimensional, weakly disordered quantum systems, displaying pointlike Fermi surface and conical intersections of the energy bands in the absence of disorder. We use rigorous renormalization group methods and supersymmetry to compute the correlation functions of the system. We prove algebraic decay of the two-point correlation function, compatible with delocalization. A main technical ingredient is the multiscale analysis of massless bosonic Gaussian integrations with purely imaginary covariances, performed via iterative stationary phase expansions.

CONSERVATION OF TOPOLOGICAL QUANTUM NUMBERS IN ENERGY BANDS

1988 ◽  
Vol 03 (18) ◽  
pp. 1839-1845 ◽  
Author(s):  
LAY NAM CHANG ◽  
YIGAO LIANG
Keyword(s):  
Classification Scheme ◽  
Energy Gap ◽  
Quantum Systems ◽  
General Context ◽  
Energy Bands ◽  
Parameter Spaces ◽  
Sum Rule ◽  
Quantum Numbers ◽  
Topological Quantum ◽  
General Parameter

Quantum systems described by parametrized Hamiltonians are studied in a general context. Within this context, the classification scheme of Avron-Seiler-Simon for non-degenerate energy bands is extended to cover general parameter spaces, while their sum rule is generalized to cover cases with degenerate bands as well. Additive topological quantum numbers are defined, and these are shown to be conserved in energy band “collisions”. The conservation laws dictate that when some invariants are non-vanishing, no energy gap can develop in a set of degenerate bands. This gives rise to a series of splitting rules.

scholarly journals Minimizing irreversible losses in quantum systems by local counterdiabatic driving

2017 ◽  
Vol 114 (20) ◽  
pp. E3909-E3916 ◽  
Author(s):  
Dries Sels ◽  
Anatoli Polkovnikov
Keyword(s):  
Variational Approach ◽  
Chaotic Systems ◽  
Chem Phys ◽  
Quantum Systems ◽  
Particle Systems ◽  
Coupling Constant ◽  
Quantum Annealing ◽  
Physical Constraints ◽  
Adiabatic Dynamics

Counterdiabatic driving protocols have been proposed [Demirplak M, Rice SA (2003) J Chem Phys A 107:9937–9945; Berry M (2009) J Phys A Math Theor 42:365303] as a means to make fast changes in the Hamiltonian without exciting transitions. Such driving in principle allows one to realize arbitrarily fast annealing protocols or implement fast dissipationless driving, circumventing standard adiabatic limitations requiring infinitesimally slow rates. These ideas were tested and used both experimentally and theoretically in small systems, but in larger chaotic systems, it is known that exact counterdiabatic protocols do not exist. In this work, we develop a simple variational approach allowing one to find the best possible counterdiabatic protocols given physical constraints, like locality. These protocols are easy to derive and implement both experimentally and numerically. We show that, using these approximate protocols, one can drastically suppress heating and increase fidelity of quantum annealing protocols in complex many-particle systems. In the fast limit, these protocols provide an effective dual description of adiabatic dynamics, where the coupling constant plays the role of time and the counterdiabatic term plays the role of the Hamiltonian.

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