scholarly journals Self-Organized PT-Symmetry of Exciton-Polariton Condensate in a Double-Well Potential

2021 ◽  
Vol 11 (16) ◽  
pp. 7372
Author(s):  
Panayotis A. Kalozoumis ◽  
David Petrosyan
Keyword(s):  
Fixed Point ◽  
Pt Symmetry ◽  
Stationary States ◽  
Stable Fixed Point ◽  
Phase Fluctuations ◽  
Self Organized ◽  
Laser Pumping ◽  
Double Well Potential ◽  
Symmetric Phase

We investigate the dynamics and stationary states of a semiconductor exciton–polariton condensate in a double-well potential. We find that upon the population build-up of the polaritons by above-threshold laser pumping, coherence relaxation due to the phase fluctuations in the polaritons drives the system into a stable fixed point corresponding to a self-organized PT-symmetric phase.

THE CRITERION FOR NONTRIVIALITY OF λϕ4 MODEL AND ITS ULTRAVIOLET STABLE FIXED POINT

1988 ◽  
Vol 03 (07) ◽  
pp. 1735-1749 ◽  
Author(s):  
GUANG-JIONG NI ◽  
SEN-YUE LOU ◽  
SU-QING CHEN
Keyword(s):  
Fixed Point ◽  
Effective Potential ◽  
Coupling Parameter ◽  
Stable Fixed Point ◽  
Running Coupling ◽  
Gaussian Effective Potential ◽  
Symmetric Phase

Using the Gaussian effective potential (GEP) method, we examine the quantized λϕ4 model in detail. The criterion for existence of either a symmetric phase or a broken phase is shown to be related to the bare parameters σ0 and λ0 in [Formula: see text]. A running coupling parameter λ with its associated B(λ) function are introduced and numerically calculated for both phases. In either case, a finite λ0 exhibits as an ultraviolet stable fixed point.

Estimation of the Stable Fixed Point of Passive Dynamic Walking with BP Neural Network

ROBOT ◽  
2010 ◽  
Vol 32 (4) ◽  
pp. 478-483 ◽  
Author(s):  
Xiuhua NI ◽  
Weishan CHEN ◽  
Junkao LIU ◽  
Shengjun SHI
Keyword(s):  
Neural Network ◽  
Fixed Point ◽  
Bp Neural Network ◽  
Stable Fixed Point ◽  
Dynamic Walking ◽  
Passive Dynamic Walking

scholarly journals THE CASE OF ASYMPTOTIC SUPERSYMMETRY

2013 ◽  
Vol 28 (14) ◽  
pp. 1350053 ◽  
Author(s):  
BRUCE L. SÁNCHEZ-VEGA ◽  
ILYA L. SHAPIRO
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Gauge Coupling ◽  
High Energy ◽  
Systematic Investigation ◽  
Coupling Constants ◽  
Scalar Coupling ◽  
Asymptotic State ◽  
Stable Fixed Point ◽  
Scalar Couplings

We start systematic investigation for the possibility to have supersymmetry (SUSY) as an asymptotic state of the gauge theory in the high energy (UV) limit, due to the renormalization group running of coupling constants of the theory. The answer on whether this situation takes place or not, can be resolved by dealing with the running of the ratios between Yukawa and scalar couplings to the gauge coupling. The behavior of these ratios does not depend too much on whether gauge coupling is asymptotically free (AF) or not. It can be shown that the UV stable fixed point for the Yukawa coupling is not supersymmetric. Taking this into account, one can break down SUSY only in the scalar coupling sector. We consider two simplest examples of such breaking, namely N = 1 supersymmetric QED and QCD. In one of the cases one can construct an example of SUSY being restored in the UV regime.

TERBIUM MOLYBDATE: GROUP THEORY AND FLUCTUATIONS

1987 ◽  
Vol 01 (05n06) ◽  
pp. 239-244
Author(s):  
SERGE GALAM
Keyword(s):  
Fixed Point ◽  
Group Theory ◽  
Parameter Space ◽  
Landau Theory ◽  
Two Dimensional ◽  
Stable Fixed Point ◽  
Theory Analysis ◽  
Continuous Transition ◽  
Dimensional Parameter ◽  
First Order

A new mechanism to explain the first order ferroelastic—ferroelectric transition in Terbium Molybdate (TMO) is presented. From group theory analysis it is shown that in the two-dimensional parameter space ordering along either an axis or a diagonal is forbidden. These symmetry-imposed singularities are found to make the unique stable fixed point not accessible for TMO. A continuous transition even if allowed within Landau theory is thus impossible once fluctuations are included. The TMO transition is therefore always first order. This explanation is supported by experimental results.

scholarly journals Chaotic Itinerancy Observed in Mutually Coupled Gaussian Maps

2018 ◽  
Vol 28 (04) ◽  
pp. 1830011
Author(s):  
Mio Kobayashi ◽  
Tetsuya Yoshinaga
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Chaotic Behavior ◽  
Periodic Points ◽  
Two Dimensional ◽  
Stable Fixed Point ◽  
Bifurcation Structure ◽  
Unstable Fixed Point ◽  
Gaussian Map ◽  
Gaussian Maps

A one-dimensional Gaussian map defined by a Gaussian function describes a discrete-time dynamical system. Chaotic behavior can be observed in both Gaussian and logistic maps. This study analyzes the bifurcation structure corresponding to the fixed and periodic points of a coupled system comprising two Gaussian maps. The bifurcation structure of a mutually coupled Gaussian map is more complex than that of a mutually coupled logistic map. In a coupled Gaussian map, it was confirmed that after a stable fixed point or stable periodic points became unstable through the bifurcation, the points were able to recover their stability while the system parameters were changing. Moreover, we investigated a parameter region in which symmetric and asymmetric stable fixed points coexisted. Asymmetric unstable fixed point was generated by the [Formula: see text]-type branching of a symmetric stable fixed point. The stability of the unstable fixed point could be recovered through period-doubling and tangent bifurcations. Furthermore, a homoclinic structure related to the occurrence of chaotic behavior and invariant closed curves caused by two-periodic points was observed. The mutually coupled Gaussian map was merely a two-dimensional dynamical system; however, chaotic itinerancy, known to be a characteristic property associated with high-dimensional dynamical systems, was observed. The bifurcation structure of the mutually coupled Gaussian map clearly elucidates the mechanism of chaotic itinerancy generation in the two-dimensional coupled map. We discussed this mechanism by comparing the bifurcation structures of the Gaussian and logistic maps.

scholarly journals DYNAMICS OF DELAY-COUPLED EXCITABLE NEURAL SYSTEMS

2009 ◽  
Vol 19 (02) ◽  
pp. 745-753 ◽  
Author(s):  
M. A. DAHLEM ◽  
G. HILLER ◽  
A. PANCHUK ◽  
E. SCHÖLL
Keyword(s):  
Nonlinear Dynamics ◽  
Fixed Point ◽  
Limit Cycles ◽  
Coupling Strength ◽  
Neural Systems ◽  
Stable Fixed Point ◽  
Bifurcation Of Limit Cycles ◽  
Large Delay ◽  
Saddle Node Bifurcation ◽  
Delay Times

We study the nonlinear dynamics of two delay-coupled neural systems each modeled by excitable dynamics of FitzHugh–Nagumo type and demonstrate that bistability between the stable fixed point and limit cycle oscillations occurs for sufficiently large delay times τ and coupling strength C. As the mechanism for these delay-induced oscillations, we identify a saddle-node bifurcation of limit cycles.

scholarly journals Pattern Completion in Symmetric Threshold-Linear Networks

2016 ◽  
Vol 28 (12) ◽  
pp. 2825-2852 ◽  
Author(s):  
Carina Curto ◽  
Katherine Morrison
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Distance Geometry ◽  
Memory Encoding ◽  
Stable Fixed Point ◽  
Pattern Completion ◽  
Linear Networks ◽  
Firing Rate Models ◽  
Classical Distance ◽  
Symmetric Networks

Threshold-linear networks are a common class of firing rate models that describe recurrent interactions among neurons. Unlike their linear counterparts, these networks generically possess multiple stable fixed points (steady states), making them viable candidates for memory encoding and retrieval. In this work, we characterize stable fixed points of general threshold-linear networks with constant external drive and discover constraints on the coexistence of fixed points involving different subsets of active neurons. In the case of symmetric networks, we prove the following antichain property: if a set of neurons [Formula: see text] is the support of a stable fixed point, then no proper subset or superset of [Formula: see text] can support a stable fixed point. Symmetric threshold-linear networks thus appear to be well suited for pattern completion, since the dynamics are guaranteed not to get stuck in a subset or superset of a stored pattern. We also show that for any graph G, we can construct a network whose stable fixed points correspond precisely to the maximal cliques of G. As an application, we design network decoders for place field codes and demonstrate their efficacy for error correction and pattern completion. The proofs of our main results build on the theory of permitted sets in threshold-linear networks, including recently developed connections to classical distance geometry.

YUKAWA MODEL IN CURVED SPACETIME

1995 ◽  
Vol 10 (15n16) ◽  
pp. 1091-1100
Author(s):  
E. ELIZALDE ◽  
S.D. ODINTSOV
Keyword(s):  
Fixed Point ◽  
Conformal Factor ◽  
Bound State ◽  
Usual Sense ◽  
Stable Fixed Point ◽  
Coupling Constant ◽  
Yukawa Model ◽  
Curved Spacetime ◽  
Cosmological Constant Problem ◽  
Njl Model

The Yukawa model in curved spacetime (renormalizable in the usual sense) is considered near the critical point, using the 1/N-expansion and renormalization group techniques. The equivalence of this model with the standard NJL model is proven. The behavior of the graviton-scalar bound state coupling constant near the ir stable fixed point ξ=1/6 is discussed. The effective potential is calculated and a dynamically generated fermionic mass is found. Some applications to quantum gravity which make explicit use of the 1/N-expansion are briefly discussed. In particular, a possible solution of the cosmological constant problem within the framework of conformal factor dynamics is pointed out.

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