Spontaneous breakdown of the time reversal symmetry

The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized $\epsilon$-prescription where the non-uniform convergence of the limit $\epsilon\to0$ leaves behind a spontaneous breakdown of the time reversal symmetry.Comment: Final version, to appear in Symmetr

Reversibility, coarse graining and the chaoticity principle

We describe a way of interpreting the chaotic principle of (ref. [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 (ref. [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.Comment: 15 pages, plain TeX, no figure

Topological spin Hall states, charged skyrmions, and superconductivity in two dimensions

We study the properties of two dimensional topological spin hall insulators which arise through spontaneous breakdown of spin symmetry in systems that are spin rotation invariant. Such a phase breaks spin rotation but not time reversal symmetry and has a vector order parameter. Skyrmion configurations in this vector order parameter are shown to have electric charge that is twice the electron charge. When the spin Hall order is destroyed by condensation of skyrmions superconductivity results. This may happen either through doping or at fixed filling by tuning interactions to close the skyrmion gap. In the latter case the superconductor- spin Hall insulator quantum phase transition can be second order even though the two phases break distinct symmetries.Comment: 4 pages, typos corrected, added a footnot

Calorimetric evidence for two phase transitions in Ba1−xKxFe2As2 with fermion pairing and quadrupling states

Materials that break multiple symmetries allow the formation of four-fermion condensates above the superconducting critical temperature (T c). Such states can be stabilized by phase fluctuations. Recently, a fermionic quadrupling condensate that breaks the Z 2 time-reversal symmetry was reported in Ba1−xKxFe2As2. A phase transition to the new state of matter should be accompanied by a specific heat anomaly at the critical temperature where Z 2 time-reversal symmetry is broken (TcZ2>Tc). Here, we report on detecting two anomalies in the specific heat of Ba1−xKxFe2As2 at zero magnetic field. The anomaly at the higher temperature is accompanied by the appearance of a spontaneous Nernst effect, indicating the breakdown of Z 2 symmetry. The second anomaly at the lower temperature coincides with the transition to a zero-resistance state, indicating the onset of superconductivity. Our data provide the first example of the appearance of a specific heat anomaly above the superconducting phase transition associated with the broken time-reversal symmetry due to the formation of the novel fermion order

Properties of dirty two-bands superconductors with repulsive interband interaction: normal modes, length scales, vortices and magnetic response

Disorder in two-band superconductors with repulsive interband interaction induces a frustrated competition between the phase-locking preferences of the various potential and kinetic terms. This frustrated interaction can result in the formation of an $s+is$ superconducting state, that breaks the time-reversal symmetry. In this paper we study the normal modes and their associated coherence lengths in such materials. We especially focus on the consequences of the soft modes stemming from the frustration and time-reversal-symmetry breakdown. We find that two-bands superconductors with such impurity-induced frustrated interactions display a rich spectrum of physical properties that are absent in their clean counterparts. It features a mixing of Leggett's and Anderson-Higgs modes, and a soft mode with diverging coherence length at the impurity-induced second order phase transition from $s_{\pm}/s_{++}$ states to the $s+is$ state. Such a soft mode generically results in long-range attractive intervortex forces that can trigger the formation of vortex clusters. We find that, if such clusters are formed, their size and internal flux density have a characteristic temperature dependence that could be probed in muon-spin-rotation experiments. We also comment on the appearance of spontaneous magnetic fields due to spatially varying impurities.Comment: Added discussion of spontaneous magnetic fields due to spatially varying impurities; Replaced with a version in print in Phys. Rev. B; 17 pages, 8 figure

Spontaneous breakdown of Lorentz symmetry in scalar QED with higher order derivatives

Scalar QED is studied with higher order derivatives for the scalar field kinetic energy. A local potential is generated for the gauge field due to the covariant derivatives and the vacuum with non-vanishing expectation value for the scalar field and the vector potential is constructed in the leading order saddle point expansion. This vacuum breaks the global gauge and Lorentz symmetry spontaneously. The unitarity of time evolution is assured in the physical, positive norm subspace and the linearized equations of motion are calculated. Goldstone theorem always keeps the radiation field massless. A particular model is constructed where the the full set of standard Maxwell equations is recovered on the tree level thereby relegating the effects of broken Lorentz symmetry to the level of radiative corrections.Comment: 14 pages, to appear in Phys. Rev.

Effective theory for deformed nuclei

Techniques from effective field theory are applied to nuclear rotation. This approach exploits the spontaneous breaking of rotational symmetry and the separation of scale between low-energy Nambu-Goldstone rotational modes and high-energy vibrational and nucleonic degrees of freedom. A power counting is established and the Hamiltonian is constructed at next-to-leading order