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.

BROKEN TIME-REVERSAL SYMMETRY AND BERRY’S PHASE

1993 ◽  
Vol 07 (11) ◽  
pp. 2109-2146 ◽  
Author(s):  
JISOON IHM
Keyword(s):  
Symmetry Breaking ◽  
Time Reversal ◽  
Geometric Phase ◽  
Slow Variable ◽  
Quantum Mechanical ◽  
Time Reversal Symmetry ◽  
Fast Variable ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Symmetry Properties

Berry’s phase is typically realized in a system consisting of fast and slow variables, when the trajectory of the slow variable makes a closed loop. The quantum mechanical phase picked up by the fast variable while the slow variable traverses the loop has turned out to produce real physical effects through quantum interference. In this article, we investigate origins of Berry’s geometric phase and show that they are in general attributable to the broken time-reversal symmetry of the system. Our analysis leads to the classification of Berry’s phase for Hamiltonian systems in terms of symmetry properties under time-reversal operations. Spontaneous time-reversal symmetry-breaking of state vectors is shown to give rise to Berry’s phase as exemplified by a quantum-mechanical rotated hoop. A system with an explicitly time-reversal symmetry-breaking Hamiltonian is also demonstrated to exhibit nontrivial Berry’s phase. The quantization of the geometric phase associated with the real two-dimensional Hamiltonian having topological singularity is explained within the same framework. The unique role of the time-reversal operator among general antiunitary operators is also discussed.

Symmetric Form of Coupling Coefficients for Single and Double Point Groups and the Application of Time-Reversal Symmetry

1974 ◽  
Vol 29 (8) ◽  
pp. 1179-1187 ◽  
Author(s):  
E. König ◽  
S. Kremer
Keyword(s):  
Time Reversal ◽  
Point Group ◽  
Time Reversal Symmetry ◽  
Coupling Coefficients ◽  
Covering Group ◽  
Group I ◽  
Symmetry Properties ◽  
Point Groups ◽  
Expansion Coefficients ◽  
Definition Of

Symmetrized coupling coefficients, the 3-Γ symbols, are investigated for an arbitrary molecular point group G ⊂ SO (3) or d G ⊂ SU(2). The definition employs the 3-j symbols of the full covering group SO (3) [or SU(2)] and the expansion coefficients of the basis functions. 〈j m | j Γ γ a〉 . Considerable simplification is achieved by taking into account time-reversal symmetry in conjunction with the lemma of Racah. It is found that the 3-Γ symbols have the same symmetry properties as the 3-j symbols of SO (3). The definition of 6-Γ symbols is likewise introduced. The treatment covers non-simply reducible groups and complex representations as well. For illustration, 3-Γ symbols of the point group I are calculated and presented.

scholarly journals A columnar liquid crystal with permanent polar order

2015 ◽  
Vol 3 (5) ◽  
pp. 985-989 ◽  
Author(s):  
J. Guilleme ◽  
J. Aragó ◽  
E. Ortí ◽  
E. Cavero ◽  
T. Sierra ◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Electric Fields ◽  
Self Assembly ◽  
Liquid Crystalline ◽  
The Self ◽  
Polar Order ◽  
Crystalline Materials ◽  
Liquid Crystalline Materials

The self-assembly of axial dipolar subphthalocyanine molecules in the presence of electric fields leads to uniaxially oriented columnar liquid crystalline materials that exhibit permanent polarization.

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 Evidence for the coexistence of time-reversal symmetry breaking and Bardeen-Cooper-Schrieffer-like superconductivity in La7Pd3

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
D. A. Mayoh ◽  
A. D. Hillier ◽  
G. Balakrishnan ◽  
M. R. Lees
Keyword(s):  
Symmetry Breaking ◽  
Time Reversal ◽  
Time Reversal Symmetry

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.

Coupled electric fields in photorefractive driven liquid crystal hybrid cells – theory and numerical simulation

2016 ◽  
Vol 24 (4) ◽  
Author(s):  
P. Moszczyński ◽  
A. Walczak ◽  
P. Marciniak
Keyword(s):  
Numerical Simulation ◽  
Laser Beam ◽  
Electric Fields ◽  
Cell Response ◽  
Liquid Crystalline ◽  
Driving Field ◽  
Self Organized ◽  
Photosensitive Polymer ◽  
Photosensitive Layer ◽  
External Driving

AbstractIn cyclic articles previously published we described and analysed self-organized light fibres inside a liquid crystalline (LC) cell contained photosensitive polymer (PP) layer. Such asymmetric LC cell we call a hybrid LC cell. Light fibre arises along a laser beam path directed in plane of an LC cell. It means that a laser beam is parallel to photosensitive layer. We observed the asymmetric LC cell response on an external driving field polarization. Observation has been done for an AC field first. It is the reason we decided to carry out a detailed research for a DC driving field to obtain an LC cell response step by step. The properly prepared LC cell has been built with an isolating layer and garbage ions deletion. We proved by means of a physical model, as well as a numerical simulation that LC asymmetric response strongly depends on junction barriers between PP and LC layers. New parametric model for a junction barrier on PP/LC boundary has been proposed. Such model is very useful because of lack of proper conductivity and charge carriers of band structure data on LC material.

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