Superconductivity with broken time-reversal symmetry

This presentation gives an overview over phenomena occurring in unconventional superconductors with broken time-reversal symmetry. The best-known effect related with broken time-reversal symmetry is intrinsic magnetism observable by μSR. In many cases this magnetism is connected to the appearance of chiral quasiparticle edge states which originate from topological properties of the superconducting order parameter. Time-reversal symmetry can also be broken only locally and has then strong influence of the local quasiparticle spectrum. The existence of vortices with fractional flux pinned strongly on domain walls in time-reversal symmetry breaking superconductors leads to unusual flux flow behavior.     

Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.     

Fluctuations in nonequilibrium systems and broken supersymmetry

The fluctuation-dissipation theorem is not expected to hold for systems that either violate detailed balance or have time-dependent or nonpotential forces. Therefore the relation between response and correlation functions should have contributions due to the nonequilibrium nature. An explicit formula for such a contribution is calculated, which in the present derivation appears as a historydependent term. These relations are the Ward-Takahashi identities of a supersymmetric formulation of the Langevin models, and the new term results from a broken supersymmetry.     

Observation of broken time-reversal symmetry with Andreev bound state tunneling spectroscopy

Quasiparticle (QP) planar tunneling spectroscopy is used to investigate the density of states (DoS) of YBa₂Cu₃O₇ (YBCO). Temperature, crystallographic orientation, doping, damage and magnetic field dependencies confirm that the observed zero-bias conductance peak (ZBCP) is an Andreev bound state (ABS), an intrinsic property of a d-wave superconducting order parameter (OP) at an interface. In zero applied field, the splitting of the ZBCP below 8 K confirms a near-surface phase transition into a superconducting state with spontaneously broken time-reversal symmetry (BTRS). Tunneling into the ABS provides a phase-sensitive spectroscopy that can be used to measure a variety of DoS properties in an unconventional superconductor.     

Pattern formations in chaotic spatio-temporal systems

Pattern formations in chaotic spatio-temporal systems modelled by coupled chaotic oscillators are investigated. We focus on various symmetry breakings and different kinds of chaos synchronization-desynchronization transitions, which lead to certain types of spontaneous spatial orderings and the emergence of some typical ordered patterns, such as rotating wave patterns with splay phase ordering (orientational symmetry breaking) and partially synchronous standing wave patterns with in-phase ordering (translational symmetry breaking). General pictures of the global behaviors of pattern formations and transitions in coupled chaotic oscillators are provided.     

Symmetry breaking in quantum chaotic systems

We show, using semiclassical methods, that as a symmetry is broken, the transition between universality classes for the spectral correlations of quantum chaotic systems is governed by the same parametrization as in the theory of random matrices. The theory is quantitatively verified for the kicked rotor quantum map. We also provide an explicit substantiation of the random matrix hypothesis, namely that in the symmetry-adapted basis the symmetry-violating operator is random.     

Optimal performance at arbitrary power of minimally nonlinear irreversible thermoelectric generators with broken time-reversal symmetry

We investigate the performance at arbitrary power of minimally nonlinear irreversible thermoelectric generators (MNITGs) with broken time-reversal symmetry within linear irreversible thermodynamics, and the efficiency of MNITGs at arbitrary power is analytically derived. Furthermore, a universal bound on the efficiency of thermoelectric generators (TGs) with broken time-reversal symmetry and the arbitrary power is obtained. Some system-specific characteristics are discussed and uncovered. A large efficiency at arbitrary power can also be achieved via the cooperative mechanism between the system parameters. Our results indicate that the broken time-reversal symmetry provides the physically allowed degrees of freedom for tuning the performance of thermoelectric devices, and the physical trade-off region between the efficiency and the power output can also offer the appropriate space for optimizing the performance of TGs.     

机电系统的统一对称性

研究机电系统的统一对称性. 由系统的Lagrange-Maxwell方程, 给出系统的统一对称性的定义和判据, 得到了系统的统一对称性导出Noether守恒量，Hojman守恒量和Mei守恒量. 举例说明结果的应用. 关键词： 机电系统 统一对称性 守恒量     

Full-order and reduced-order observer-based synchronization for chaotic systems with unknown disturbances and parameters

The Letter deals with the problem of synchronization of chaotic dynamic system with unknown disturbances and parameters based on observer. First, under some assumptions for drive system, a kind of full-order observer-based synchronization method is summarized. The response system is a robust adaptive full-order observer with adaptation laws for the unknown disturbances and parameters. Second, under the same assumptions, a reduced-order observer-based response system which can synchronize part states of drive system is developed. By choosing a special reduced-order gain matrix, the reduced-order observer-based response system is able to eliminate the influence of the unknown disturbances and parameters directly, so it is unnecessary for one to design the adaptation laws of them. Finally, some numerical simulations for Lorenz chaotic system are design and the simulation results are analyzed in detail.     

夸克与对称性自发破缺

用普通物理和原子物理的语言论述了对称性破缺机制和理论模型,介绍了2008年度诺贝尔物理学获奖者小林诚(Makoto Kobayashi)、益川敏英(Toshihide Maskawa)关于弱相互作用的理论模型(KM模型)和对称性破缺的起源,它是对电弱统一理论的完美补充;详细分析了在微观粒子世界系列实验中对称性自发破缺和夸克的发现.     

Lie symmetry theorem of fractional nonholonomic systems

The Lie symmetry theorem of fractional nonholonomic systems in terms of combined fractional derivatives is estab- lished, and the fractional Lagrange equations are obtained by virtue of the d＇Alembert-Lagrange principle with fractional derivatives. As the Lie symmetry theorem is based on the invariance of differential equations under infinitesimal trans- formations, by introducing the differential operator of infinitesimal generators, the determining equations are obtained. Furthermore, the limit equations, the additional restriction equations, the structural equations, and the conserved quantity of Lie symmetry are acquired. An example is presented to illustrate the application of results.     

Disordered two-dimensional electron systems with chiral symmetry

We review the results of our recent numerical investigations on the electronic properties of disordered two dimensional systems with chiral unitary, chiral orthogonal, and chiral symplectic symmetry. Of particular interest is the behavior of the density of states and the logarithmic scaling of the smallest Lyapunov exponents in the vicinity of the chiral quantum critical point in the band center at E=0. The observed peaks or depressions in the density of states, the distribution of the critical conductances, and the possible non-universality of the critical exponents for certain chiral unitary models are discussed.     

On systems having Poincaré and Galileo symmetry

Using the wave equation in d≥1$d\ge 1$ space dimensions it is illustrated how dynamical equations may be simultaneously Poincaré and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d=1$d=1$ the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated with the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d>1$d>1$ is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwell’s equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics.     

Nambu力学系统的Lie对称性及其守恒量

讨论了Nambu力学系统的Lie对称性;建立了系统Lie对称性的确定方程;得到了该对称性引起的守恒量;研究了Lie对称性逆问题. 并以Euler方程为例说明了本文的主要结果. 关键词： Nambu力学系统 Lie对称性 守恒量     

Quantum fluctuations in quantum lattice systems with continuous symmetry

We discuss conditions for the absence of spontaneous breakdown of continuous symmetries in quantum lattice systems atT=0. Our analysis is based on Pitaevskii and Stringari's idea that the uncertainty relation can be employed to show quantum fluctuations. For one-dimensional systems, it is shown that the ground state is invariant under a continuous transformation if a certain uniform susceptibility is finite. For the two- and three-dimensional systems, it is shown that truncated correlation functions cannot decay any more rapidly than|r| ^–d+1 whenever the continuous symmetry is spontaneously broken. Both of these phenomena occur owing to quantum fluctuations. Our theorems cover a wide class of quantum lattice systems having not-too-long-range interactions.     

A simple observer design of the generalized Lorenz chaotic systems

In this Letter, the generalized Lorenz chaotic system is considered and the state observation problem of such a system is investigated. Based on the time-domain approach, a simple observer for the generalized Lorenz chaotic system is developed to guarantee the global exponential stability of the resulting error system. Moreover, the guaranteed exponential convergence rate can be correctly estimated. Finally, a numerical example is given to show the effectiveness of the obtained result.     

Conductance fluctuations in disordered superconductors with broken time-reversal symmetry near two dimensions

We extend the analysis of the conductance fluctuations in disordered metals by Altshuler, Kravtsov, and Lerner (AKL) to disordered superconductors with broken time-reversal symmetry in d=(2+?)$d=(2+\mathrm{?})$ dimensions (symmetry classes C and D of Altland and Zirnbauer). Using a perturbative renormalization group analysis of the corresponding non-linear sigma model (NLσM) we compute the anomalous scaling dimensions of the dominant scalar operators with 2s   gradients to one-loop order. We show that, in analogy with the result of AKL for ordinary, metallic systems (Wigner–Dyson classes), an infinite number of high-gradient operators would become relevant (in the renormalization group sense) near two dimensions if contributions beyond one-loop order are ignored. We explore the possibility to compare, in symmetry class D, the ?=(2−d)$\mathrm{?}=(2-d)$ expansion in d<2$d<2$ with exact results in one dimension. The method we use to perform the one-loop renormalization analysis is valid for general symmetric spaces of Kähler type, and suggests that this is a generic property of the perturbative treatment of NLσMs defined on Riemannian symmetric target spaces.