Time reversal and symmetries of time correlation functions

ABSTRACT

The time reversal invariance of classical dynamics is reconsidered in this paper with specific focus on its consequences for time correlation functions and associated properties such as transport coefficients. We show that, under fairly common assumptions on the interparticle potential, an isolated Hamiltonian system obeys more than one time reversal symmetry and that this entails non trivial consequences. Under an isotropic and homogeneous potential, in particular, eight valid time reversal operations exist. The presence of external fields that reduce the symmetry of space decreases this number, but does not necessarily impair all time reversal symmetries. Thus, analytic predictions of symmetry properties of time correlation functions and, in some cases, even of their null value are still possible. The noteworthy case of a constant external magnetic field, usually assumed to destroy time reversal symmetry, is considered in some detail. We show that, in this case too, some of the new time reversal operations hold, and that this makes it possible to derive relevant properties of correlation functions without the uninteresting inversion of the direction of the magnetic field commonly enforced in the literature.     

Topological solitons in three-band superconductors with broken time reversal symmetry

We show that three-band superconductors with broken time reversal symmetry allow magnetic flux-carrying stable topological solitons. They can be induced by fluctuations or quenching the system through a phase transition. It can provide an experimental signature of the time reversal symmetry breakdown.     

SU(2) symmetry in a Hubbard model with spin-orbit coupling

We study the underlying symmetry in a spin-orbit coupled tight-binding model with Hubbard interaction. It is shown that, in the absence of the on-site interaction, the system possesses the SU(2) symmetry arising from the time reversal symmetry. The influence of the on-site interaction on the symmetry depends on the topology of the networks: The SU(2) symmetry is shown to be the spin rotation symmetry of a simply-connected lattice even in the presence of the Hubbard interaction. On the contrary, the on-site interaction breaks the SU(2) symmetry of a multi-connected lattice. This fact indicates that a discrete spin-orbit coupled system has exclusive features from its counterpart in a continuous system. The obtained rigorous result is illustrated by a simple ring system.     

Electromagnetic retarded interaction and symmetry violation of time reversal in high order stimulated radiation and absorption processes of light

It has been proved that when the retarded effect (or multiple moment effect) of radiation fields is taken into account, the high order stimulated radiation and stimulated absorption probabilities of light are not the same so that time reversal symmetry would be violated, though the Hamiltonian of electromagnetic interaction is still unchanged under time reversal. The reason to cause time reversal symmetry violation is that certain filial or partial transition processes of bound atoms are forbidden or cannot be achieved due to the law of energy conservation and the special states of atoms themselves. These restrictions would cause the symmetry violation of time reversal of other filial or partial transition processes which can be actualized really. The symmetry violation is also relative to the asymmetry of initial states of bound atoms before and after time reversal. For the electromagnetic interaction between non-bound atoms and radiation field, there is no such kind of symmetry violation of time reversal. In this way, the current formula on the parameters of stimulated radiation and absorption of light with time reversal symmetry should be revised. A more reliable foundation can be established for the theories of laser and nonlinear optics in which non-equilibrium processes are involved.     

Reversibility, Coarse Graining and the Chaoticity Principle

We describe a way of interpreting the chaotic principle of [GC1] more extensively than it was meant in the original works. Mathematically the analysis is based on the dynamical notions of Axiom A and Axiom B and on the notion of Axiom C, that we introduce arguing that it is suggested by the results of an experiment ([BGG]) on chaotic motions. Physically we interpret a breakdown of the Anosov property of a time reversible attractor (replaced, as a control parameter changes, by an Axiom A property) as a spontaneous breakdown of the time reversal symmetry: the relation between time reversal and the symmetry that remains after the breakdown is analogous to the breakdown of T-invariance while TCP still holds. Received: 28 February 1996 / Accepted: 12 February 1997     

Nonlocal Symmetry and Explicit Solution of the Alice-Bob Modified Korteweg-de Vries Equation

Nonlocal symmetry and explicit solution of the integrable Alice-Bob modified Korteweg-de Vries (ABmKdV) equation is discussed, which has been established by the aid of the shifted parity and delayed time reversal to describe two-place events. Based on the Lax pair which contains the two-order partial derivative, the Lie symmetry group method is successfully applied to find the exact invariant solution for the AB-mKdV equation with nonlocal symmetry by introducing one suitable auxiliary variable. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to some specific functions are derived. Figures show the physical phenomenon, that is, "the shifted parity and delayed time reversal to describe two-place events".     

Nonlocal Symmetry and Explicit Solution of the Alice-Bob Modified Korteweg-de Vries Equation

Nonlocal symmetry and explicit solution of the integrable Alice-Bob modified Korteweg-de Vries(ABm Kd V) equation is discussed, which has been established by the aid of the shifted parity and delayed time reversal to describe two-place events. Based on the Lax pair which contains the two-order partial derivative, the Lie symmetry group method is successfully applied to find the exact invariant solution for the AB-m Kd V equation with nonlocal symmetry by introducing one suitable auxiliary variable. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to some specific functions are derived. Figures show the physical phenomenon, that is, "the shifted parity and delayed time reversal to describe two-place events".     

The explicit symmetry breaking solutions of the Kadomtsev-Petviashvili equation

To describe two correlated events, the Alice–Bob (AB) systems were constructed by Lou through the symmetry of the shifted parity, time reversal and charge conjugation. In this paper, the coupled AB system of the Kadomtsev–Petviashvili equation, which is a useful model in natural science, is established. By introducing an extended Bäcklund transformation and its bilinear formation, the symmetry breaking soliton, lump and breather solutions of this system are derived with the aid of some ansatze functions. Figures show these fascinating symmetry breaking structures of the explicit solutions.     

Quantum scattering in the strip: From ballistic to localized regimes

Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition between the ballistic and the localized regimes. By considering the cylinder geometry and introducing the magnetic flux we are able to study time reversal symmetry breaking in the system. Both macroscopic (conductance) and microscopic (eigenphases distribution, statistics of S-matrix elements) characteristics of the system are examined. Received: 28 January 1998 / Revised: 16 June 1998 / Accepted: 6 July 1998     

时间反演对称和非平衡统计定常态(Ⅰ)

本文是作者从微观量子统计理论出发应用微观可逆性原理讨论非平衡统计定常态普遍性质的第一部份。文中给出了非平衡量子统计格林函数(闭路格林函数)在定常态上关于时间反演对称的表达方式。把生成泛函技术和时间反演对称结合起来,得到了具有时间反演对称性的非平衡统计定常态上统计格林函数和顶点函数所满足的时间反演对称关系。 关键词：     

Tunable $\chi /\mathcal {P}\mathcal {T}$ Symmetry in Noisy Graphene

We investigate the resonant regime of a mesoscopic cavity made of graphene or a doped beam splitter. Using Non-Hermitian Quantum Mechanics, we consider the Bender-Boettcher assumption that a system must obey parity and time reversal symmetry. Therefore, we describe such system by coupling chirality, parity, and time reversal symmetries through the scattering matrix formalism and apply it in the shot noise functions, also derived here. Finally, we show how to achieve the resonant regime only by setting properly the parameters concerning the chirality and the PT symmetry.     

On the law of increasing entropy and the cause of the dynamics irreversibility of quantum systems

It has been shown that time reversal symmetry breaking in the dynamics of large systems originates from symmetry breaking in the occupation of the Hilbert space. The states ?, for which the entropy of the system (sub-system) increases, are automatically created in nature or can be prepared experimentally, in contrast to the respective complex-conjugate states (?*), for which the entropy decreases (although formally, according to the superposition principle, they can exist). It is indicated that, in the general case, the dynamics reversal of unknown states is impossible because the complex conjugation operator is antilinear. The complexity of reversal of the known state is exponential in the typical case of a large system. The formulated statements are illustrated by simple models.     

Time reversed wave propagation experiments in chaotic micro-structured cavities

The elastic wave propagation in strongly scattering solid-state cavity consisting of a thin micro-patterned silicon wafer is studied experimentally. The chaotic behavior is induced by the irregular boundary of the cavity and/or by fabricating patterns of small holes in the wafer by laser machining. The pattern and hole size are designed with length scales matching the wavelength 相似文献   

Magnetization reversal in the pinned layer of CoFe/PtMn bilayers

The magnetization reversal of the ferromagnetic (FM) layer in CoFe/PtMn exchange-coupled bilayer films has been investigated using bulk magnetometry. These films exhibit very complex angular dependence and the easy axis is perpendicular to the field applied during deposition and post-annealing. Holding the film at negative saturation of the FM layer for up to 17 h results in no change in the exchange field. We believe that this is a thermally stable exchange-coupled system. Only limited thermal activation with a small time constant appears and no thermally activated reversal of the antiferromagnetic layer with a large time constant exits.     

Optical activity and time reversal

The rôle of time reversal symmetry in natural and magnetic optical activity is discussed. Natural optical rotation is shown to be generated by an anti-hermitian odd parity time-even operator and magnetic optical rotation by an anti-hermitian even parity time-odd operator. This shows that lack of time reversal invariance is not the source of natural optical rotation and that free atoms can show natural optical rotation without violating reversality, which leads to a fundamental distinction between the conditions necessary for natural optical rotation and a permanent space-fixed electric dipole moment. General transition optical activity and polarizability tensors between components of degenerate states are discussed with reference to possible new Raman experiments and new contributions to discriminating intermolecular forces between chiral molecules. Time reversal symmetry also leads to a new criterion for chiral objects and to the concept that natural optical activity provides an example of spontaneous symmetry breaking with respect to CP.     

Time reversal symmetry in light scattering by excitations in a film

We present a general symmetry argument for light scattering by excitations in an insulator film. The analysis holds for bulk continuum, guided and surface excitations.The main results represent a simplification of the theory and a better understanding for the time reversal properties of the system. Those properties hold both for forward and backward scatering, and are independent of the substrate upon which the film is deposited. We show that the asymmetry in the shape of the cross-section which is common to many experimental situations is in fact a consequence of the time reversal properties of the system.     

N = 1 Dualities for Exceptional Gauge Groups and Quantum Global Symmetries

We discuss our attempts to generalize the known examples of dualities in N = 1 supersymmetric gauge theories to exceptional gauge groups. We derive some dual pairs from known examples connected to exceptional groups and find an interesting phenomenon: sometimes the full global symmetry is “hidden” on the magnetic side. It is not realized as a symmetry on the fundamental fields in the Lagrangian. Rather, it emerges as a symmetry of the quantum theory. We then focus on an approach based on self-dual models. We construct duals for some very special matter content of E₇, E₆ and F₄. Again we find that the full global symmetry is not realized on the fundamental fields.     

Time reversal during magnetization of gas atoms by a resonant light pulse

The optically induced magnetic moment of a stationary atom is calculated as a function of time and the resonance detuning ω-ω _ba to within a constant factor having the dimensions of a magnetic moment based on the symmetry of an atom in the field of a resonant light pulse and symmetry with respect to time reversal including the initial conditions. The even dependence of the optically induced magnetic moment on ω-ω _ba for an elliptically polarized pulse with an isotropic initial state of the atom and its odd dependence on ω-ω _ba in the case of a linearly polarized pulsed with an anisotropic initial state in the atom’s alignment are shown to be consequences of symmetry with respect to time reversal and the initial conditions. This behavior is retained even after passage of the light pulse, when the resulting relaxation destroys the time reversal symmetry. The optically induced magnetization of an atomic gas is found to have analogous properties. Zh. éksp. Teor. Fiz. 112, 453–469 (August 1997)     

Criteria for the absence of quantum fluctuations after spontaneous symmetry breaking

The lowest-energy state of a macroscopic system in which symmetry is spontaneously broken, is a very stable wavepacket centered around a spontaneously chosen, classical direction in symmetry space. However, for a Heisenberg ferromagnet the quantum groundstate is exactly the classical groundstate, there are no quantum fluctuations. This coincides with seven exceptional properties of the ferromagnet, including spontaneous time-reversal symmetry breaking, a reduced number of Nambu–Goldstone modes and the absence of a thin spectrum (Anderson tower of states). Recent discoveries of other non-relativistic systems with fewer Nambu–Goldstone modes suggest these specialties apply there as well. I establish precise criteria for the absence of quantum fluctuations and all the other features. In particular, it is not sufficient that the order parameter operator commutes with the Hamiltonian. It leads to a measurably larger coherence time of superpositions in small but macroscopic systems.