scholarly journals Action Functional for a Particle with Damping

2019 ◽  
Vol 4 (3) ◽  
pp. 81 ◽  
Author(s):  
Federico de Bettin ◽  
Alberto Cappellaro ◽  
Luca Salasnich
Keyword(s):  
Effective Action ◽  
Time Reversal ◽  
Equation Of Motion ◽  
Harmonic Oscillators ◽  
Time Reversal Symmetry ◽  
Action Functional ◽  
Weakly Coupled ◽  
Dissipative Equation

In this brief report we discuss the action functional of a particle with damping, showing that it can be obtained from the dissipative equation of motion through a modification which makes the new dissipative equation invariant for time reversal symmetry. This action functional is exactly the effective action of Caldeira-Leggett model but, in our approach, it is derived without the assumption that the particle is weakly coupled to a bath of infinite harmonic oscillators.

scholarly journals The Wigner-Dunkl-Newton mechanics with time-reversal symmetry

2020 ◽  
Vol 66 (3 May-Jun) ◽  
pp. 308
Author(s):  
W. Sang Chung ◽  
H. Hassanabadi
Keyword(s):  
Time Reversal ◽  
Hamiltonian Formalism ◽  
Equation Of Motion ◽  
Time Reversal Symmetry ◽  
Elementary Functions ◽  
Exponential Functions ◽  
Hyperbolic Functions ◽  
Newton Equation

In this paper we use the Dunkl derivative with respect to time to construct theWigner-Dunkl-Newton mechanics with time-reversal symmetry. We deflne the WignerDunkl-Newton velocity and Wigner-Dunkl-Newton acceleration and construct the WignerDunkl-Newton equation of motion. We also discuss the Hamiltonian formalism in theWigner-Dunkl-Newton mechanics. We discuss some deformed elementary functions suchas the ”-deformed exponential functions, ”-deformed hyperbolic functions and ”-deformedtrigonometric functions. Using these we solve some problems in on dimensional WignerDunkl-Newton mechanics mechanics.

scholarly journals Odd Willis coupling induced by broken time-reversal symmetry

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Li Quan ◽  
Simon Yves ◽  
Yugui Peng ◽  
Hussein Esfahlani ◽  
Andrea Alù
Keyword(s):  
Time Reversal ◽  
Time Reversal Symmetry ◽  
Acoustic Metamaterials ◽  
Asymmetric Structures ◽  
Sound Control ◽  
Wavefront Shaping ◽  
Scattering Response ◽  
Symmetric Structures ◽  
Signal Routing ◽  
Broad Interest

AbstractWhen sound interacts with geometrically asymmetric structures, it experiences coupling between pressure and particle velocity, known as Willis coupling. While in most instances this phenomenon is perturbative in nature, tailored asymmetries combined with resonances can largely enhance it, enabling exotic acoustic phenomena. In these systems, Willis coupling obeys reciprocity, imposing an even symmetry of the Willis coefficients with respect to time reversal and the impinging wave vector, which translates into stringent constraints on the overall scattering response. In this work, we introduce and experimentally observe a dual form of acoustic Willis coupling, arising in geometrically symmetric structures when time-reversal symmetry is broken, for which the pressure-velocity coupling is purely odd-symmetric. We derive the conditions to maximize this effect, we experimentally verify it in a symmetric subwavelength scatterer biased by angular momentum, and we demonstrate the opportunities for sound scattering enabled by odd Willis coupling. Our study opens directions for acoustic metamaterials, with direct implications for sound control, non-reciprocal scattering, wavefront shaping and signal routing, of broad interest also for nano-optics, photonics, elasto-dynamics, and mechanics.

scholarly journals Wiedemann-Franz laws and Sl(2, ℤ) duality in AdS/CMT holographic duals and one-dimensional effective actions for them

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Dmitry Melnikov ◽  
Horatiu Nastase
Keyword(s):  
Quantum Hall Effect ◽  
Effective Action ◽  
Transport Coefficients ◽  
Quantum Hall ◽  
Dual Theory ◽  
One Dimensional ◽  
Integer Quantum Hall Effect ◽  
Weakly Coupled ◽  
Holographic Duals ◽  
Integer Quantum

Abstract In this paper we study the Wiedemann-Franz laws for transport in 2+1 dimensions, and the action of Sl(2, ℤ) on this transport, for theories with an AdS/CMT dual. We find that Sl(2, ℤ) restricts the RG-like flow of conductivities and that the Wiedemann-Franz law is $$ \overline{L}=\overline{\kappa}/\left( T\sigma \right)={cg}_4^2\uppi /3 $$ L ¯ = κ ¯ / Tσ = cg 4 2 π / 3 , from the weakly coupled gravity dual. In a self-dual theory this value is also the value of L = κ/(Tσ) in the weakly coupled field theory description. Using the formalism of a 0+1 dimensional effective action for both generalized SY Kq models and the AdS4 gravity dual, we calculate the transport coefficients and show how they can be matched at large q. We construct a generalization of this effective action that is invariant under Sl(2, ℤ) and can describe vortex conduction and integer quantum Hall effect.

scholarly journals Symmetry aspects in the macroscopic dynamics of magnetorheological gels and general liquid crystalline magnetic elastomers

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Harald Pleiner ◽  
Helmut R. Brand
Keyword(s):  
Electric Fields ◽  
Time Reversal ◽  
Liquid Crystalline ◽  
Second Law Of Thermodynamics ◽  
Time Reversal Symmetry ◽  
Local Conservation ◽  
Continuous Symmetry ◽  
Polar Order ◽  
Preferred Direction ◽  
Symmetry Properties

Abstract We investigate theoretically the macroscopic dynamics of various types of ordered magnetic fluid, gel, and elastomeric phases. We take a symmetry point of view and emphasize its importance for a macroscopic description. The interactions and couplings among the relevant variables are based on their individual symmetry behavior, irrespective of the detailed nature of the microscopic interactions involved. Concerning the variables we discriminate between conserved variables related to a local conservation law, symmetry variables describing a (spontaneously) broken continuous symmetry (e.g., due to a preferred direction) and slowly relaxing ones that arise from special conditions of the system are considered. Among the relevant symmetries, we consider the behavior under spatial rotations (e.g., discriminating scalars, vectors or tensors), under spatial inversion (discriminating e.g., polar and axial vectors), and under time reversal symmetry (discriminating e.g., velocities from polarizations, or electric fields from magnetic ones). Those symmetries are crucial not only to find the possible cross-couplings correctly but also to get a description of the macroscopic dynamics that is compatible with thermodynamics. In particular, time reversal symmetry is decisive to get the second law of thermodynamics right. We discuss (conventional quadrupolar) nematic order, polar order, active polar order, as well as ferromagnetic order and tetrahedral (octupolar) order. In a second step, we show some of the consequences of the symmetry properties for the various systems that we have worked on within the SPP1681, including magnetic nematic (and cholesteric) elastomers, ferromagnetic nematics (also with tetrahedral order), ferromagnetic elastomers with tetrahedral order, gels and elastomers with polar or active polar order, and finally magnetorheological fluids and gels in a one- and two-fluid description.

scholarly journals Unsplit superconducting and time reversal symmetry breaking transitions in Sr2RuO4 under hydrostatic pressure and disorder

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Vadim Grinenko ◽  
Debarchan Das ◽  
Ritu Gupta ◽  
Bastian Zinkl ◽  
Naoki Kikugawa ◽  
...  
Keyword(s):  
Hydrostatic Pressure ◽  
Symmetry Breaking ◽  
Time Reversal ◽  
Order Parameter ◽  
Muon Spin Rotation ◽  
Horizontal Line ◽  
Time Reversal Symmetry ◽  
Zero Field ◽  
Symmetry Protected ◽  
Line Node

AbstractThere is considerable evidence that the superconducting state of Sr2RuO4 breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking, its onset temperature, TTRSB, is generally found to match the critical temperature, Tc, within resolution. In combination with evidence for even parity, this result has led to consideration of a dxz ± idyz order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding TTRSB = Tc, but it has a hard-to-explain horizontal line node at kz = 0. Therefore, s ± id and d ± ig order parameters are also under consideration. These avoid the horizontal line node, but require tuning to obtain TTRSB ≈ Tc. To obtain evidence distinguishing these two possible scenarios (of symmetry-protected versus accidental degeneracy), we employ zero-field muon spin rotation/relaxation to study pure Sr2RuO4 under hydrostatic pressure, and Sr1.98La0.02RuO4 at zero pressure. Both hydrostatic pressure and La substitution alter Tc without lifting the tetragonal lattice symmetry, so if the degeneracy is symmetry-protected, TTRSB should track changes in Tc, while if it is accidental, these transition temperatures should generally separate. We observe TTRSB to track Tc, supporting the hypothesis of dxz ± idyz order.

Tests of Time-Reversal Symmetry in Compound-Nucleus Reactions

1986 ◽  
Vol 56 (19) ◽  
pp. 2012-2015 ◽  
Author(s):  
D. Boosé ◽  
H. L. Harney ◽  
H. A. Weidenmüller
Keyword(s):  
Compound Nucleus ◽  
Time Reversal ◽  
Time Reversal Symmetry
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