Elementary modes of coupled oscillators as whispering-gallery microresonators

2015 ◽  
Vol 30 (39) ◽  
pp. 1550193 ◽  
Author(s):  
Rabin Banerjee ◽  
Pradip Mukherjee
Keyword(s):  
Phase Transition ◽  
Time Reversal ◽  
Coupled Oscillators ◽  
Quantum Physics ◽  
Whispering Gallery ◽  
Physical Picture ◽  
Elementary Modes

We obtain the elementary modes of a system of parity-time reversal (PT)-symmetric coupled oscillators with balanced loss and gain. These modes are used to give a physical picture of the phase transition recently reported [C. M. Bender, M. Gianfreda, B. Peng, S. K. Özdemir and L. Yang, Phys. Rev. A 88, 062111 (2013); L. Yang, S. K. Özdemir and B. Peng, 12th Int. Workshop and Conf. Pseudo-Hermitian Hamiltonians in Quantum Physics, Istanbul, Turkey, July 2013; B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender and L. Yang, Nat. Phys. 10, 394 (2014)] in experiments with whispering-gallery microresonators.

scholarly journals Energy dissipation and fluctuations in a driven liquid

2018 ◽  
Vol 115 (14) ◽  
pp. 3569-3574 ◽  
Author(s):  
Clara del Junco ◽  
Laura Tociu ◽  
Suriyanarayanan Vaikuntanathan
Keyword(s):  
Phase Transition ◽  
Steady State ◽  
Time Reversal ◽  
Time Dependent ◽  
Time Reversal Symmetry ◽  
Nonequilibrium Systems ◽  
Minimal Models ◽  
Stochastic Thermodynamics ◽  
Periodic Steady State ◽  
Time Periodic

Minimal models of active and driven particles have recently been used to elucidate many properties of nonequilibrium systems. However, the relation between energy consumption and changes in the structure and transport properties of these nonequilibrium materials remains to be explored. We explore this relation in a minimal model of a driven liquid that settles into a time periodic steady state. Using concepts from stochastic thermodynamics and liquid state theories, we show how the work performed on the system by various nonconservative, time-dependent forces—this quantifies a violation of time reversal symmetry—modifies the structural, transport, and phase transition properties of the driven liquid.

scholarly journals Phase Transition and Hysteresis in an Ensemble of Stochastic Spiking Neurons

2007 ◽  
Vol 19 (11) ◽  
pp. 3011-3050 ◽  
Author(s):  
Andreas Kaltenbrunner ◽  
Vicenç Gómez ◽  
Vicente López
Keyword(s):  
Phase Transition ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Stochastic Dynamics ◽  
Upper And Lower Bounds ◽  
Critical Coupling ◽  
Sustained Activity ◽  
Large Ensembles ◽  
Coupling Strengths ◽  
Pulse Coupled Oscillators

An ensemble of stochastic nonleaky integrate-and-fire neurons with global, delayed, and excitatory coupling and a small refractory period is analyzed. Simulations with adiabatic changes of the coupling strength indicate the presence of a phase transition accompanied by a hysteresis around a critical coupling strength. Below the critical coupling production of spikes in the ensemble is governed by the stochastic dynamics, whereas for coupling greater than the critical value, the stochastic dynamics loses its influence and the units organize into several clusters with self-sustained activity. All units within one cluster spike in unison, and the clusters themselves are phase-locked. Theoretical analysis leads to upper and lower bounds for the average interspike interval of the ensemble valid for all possible coupling strengths. The bounds allow calculating the limit behavior for large ensembles and characterize the phase transition analytically. These results may be extensible to pulse-coupled oscillators.

scholarly journals Solution to the Time-Dependent Coupled Harmonic Oscillators Hamiltonian with Arbitrary Interactions

2019 ◽  
Vol 1 (1) ◽  
pp. 82-90 ◽  
Author(s):  
Alejandro R. Urzúa ◽  
Irán Ramos-Prieto ◽  
Manuel Fernández-Guasti ◽  
Héctor M. Moya-Cessa
Keyword(s):  
Coupled Oscillators ◽  
Quantum Physics ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Unitary Operators ◽  
Orthogonal Functions ◽  
Molecular Chemistry ◽  
Coupled Harmonic Oscillators ◽  
Generalized Orthogonal

We show that by using the quantum orthogonal functions invariant, we found a solution to coupled time-dependent harmonic oscillators where all the time-dependent frequencies are arbitrary. This system may be found in many applications such as nonlinear and quantum physics, biophysics, molecular chemistry, and cosmology. We solve the time-dependent coupled harmonic oscillators by transforming the Hamiltonian of the interaction using a set of unitary operators. In passing, we show that N time-dependent and coupled oscillators have a generalized orthogonal functions invariant from which we can write a Ermakov–Lewis invariant.

scholarly journals Two-boson quantum interference in time

2020 ◽  
Vol 117 (52) ◽  
pp. 33107-33116
Author(s):  
Nicolas J. Cerf ◽  
Michael G. Jabbour
Keyword(s):  
Time Reversal ◽  
Quantum Interference ◽  
Quantum Physics ◽  
Beam Splitter ◽  
Underlying Mechanism ◽  
Pauli Principle ◽  
Quantum Particles ◽  
Identical Quantum ◽  
Quantum Amplifier ◽  
Fundamental Mechanism

The celebrated Hong–Ou–Mandel effect is the paradigm of two-particle quantum interference. It has its roots in the symmetry of identical quantum particles, as dictated by the Pauli principle. Two identical bosons impinging on a beam splitter (of transmittance 1/2) cannot be detected in coincidence at both output ports, as confirmed in numerous experiments with light or even matter. Here, we establish that partial time reversal transforms the beam splitter linear coupling into amplification. We infer from this duality the existence of an unsuspected two-boson interferometric effect in a quantum amplifier (of gain 2) and identify the underlying mechanism as time-like indistinguishability. This fundamental mechanism is generic to any bosonic Bogoliubov transformation, so we anticipate wide implications in quantum physics.

MOLECULES AS QUANTUM SHAPES AND HOW THEY VIOLATE P AND T

1992 ◽  
Vol 07 (09) ◽  
pp. 2087-2107 ◽  
Author(s):  
A.P. BALACHANDRAN ◽  
A. SIMONI ◽  
D.M. WITT
Keyword(s):  
Time Reversal ◽  
Quantum Physics ◽  
Gauge Theories ◽  
Dimensional Euclidean Space ◽  
Model Description ◽  
Molecular Physics ◽  
Collective Models ◽  
Quantum Theories ◽  
Oppenheimer Approximation ◽  
Left And Right

A geometric shape is a rigid shape in n-dimensional Euclidean space. These shapes commonly occur in the Born-Oppenheimer approximation in molecular physics, and collective models of nuclei. Abelian and non-Abelian generalizations of the vacuum angle of gauge theories are realized in the quantum theory of shapes. In this paper, such generalizations are presented in the language of modern quantum physics and it is shown that parity, [Formula: see text], and time reversal, [Formula: see text], are violated in certain of these quantum theories. However, the combined symmetry [Formula: see text] of parity composed with time reversal generally remains a good symmetry, just as in gauge theories. The exceptions are the quantum theories of staggered conformations which can violate only [Formula: see text]. The mechanism responsible for the loss of these symmetries is a generalization of the vacuum angle mechanism for the same effect. An important result of the present analysis is the demonstration that geometric shapes, molecules in the Born-Oppenheimer approximation, and nuclei in the collective model description furnish concrete systems which upon quantization discriminate between left- and right-handed coordinates even though this distinction is entirely absent in their classical descriptions.

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