Anomalous dynamical response of non-Hermitian topological phases

Composite topological phases with intriguing topology like M${\"o}$bius strips emerge in sublattice symmetric non-Hermitian systems due to spontaneous breaking of time-reversal symmetry at some parameter regime. While these phases have been characterized by nonadiabatic complex geometric phases of multiple participating complex bands, the physical properties of these phases largely remain unknown. We explore the dynamical response of these phases by studying Loschmidt echo from an initial state of the Hermitian Su-Schrieffer-Heeger (SSH) model, which is evolved by a non-Hermitian SSH Hamiltonian after a sudden quench in parameters. Topology-changing quenches display non-analytical temporal behavior of return rates (logarithm of the Loschmidt echo) for the non-Hermitian SSH Hamiltonian in the trivial, M${\"o}$bius and topological phase. Moreover, the dynamical topological order parameter appears only at one side of the Brillouin zone for the M${\"o}$bius phase case in contrast to both sides of the Brillouin zone for quench by the trivial and topological phase of the non-Hermitian SSH model. The last feature is a dynamical signature of different symmetry constraints on the real and imaginary parts of the complex bands in the M${\"o}$bius phase.Comment: 10 pages, 6 figure

Transport in a long-range Kitaev ladder: role of Majorana and subgap Andreev states

We study local and non-local transport across a two-leg long-range Kitaev ladder connected to two normal metal leads. We focus on the role of the constituent Majorana fermions and the subgap Andreev states. The double degeneracy of Majorana fermions of the individual legs of the ladder gets lifted by a coupling between the two leading to the formation of Andreev bound states. The coupling can be induced by a superconducting phase difference between the two legs of the ladder accompanied by a finite inter-leg hopping. Andreev bound states formed strongly enhance local Andreev reflection. When the ladder and normal metal are weakly coupled, the Andreev bound states, which are the controlling factor, result in weak nonlocal scattering. In sharp contrast, when the ladder - normal metal interface is transparent to electron flow, we find that the subgap Andreev states enhance nonlocal conductance strongly. The features in the local and nonlocal conductances resemble the spectrum of the isolated ladder. Long-range pairing helps lift the degeneracy of the Majorana modes, makes them less localized, and thus inhibits local transport, while aiding non-local transport. In particular, long-range pairing alone (without a superconducting phase difference) can enhance crossed Andreev reflection.Comment: 11 pages, 9 figure

Topology of multipartite non-Hermitian one-dimensional systems

The multipartite non-Hermitian Su-Schrieffer-Heeger model is explored as a prototypical example of one-dimensional systems with several sublattice sites for unveiling intriguing insulating and metallic phases with no Hermitian counterparts. These phases are characterized by composite cyclic loops of multiple complex-energy bands encircling single or multiple exceptional points (EPs) on the parametric space of real and imaginary energy. We show the topology of these composite loops is similar to well-known topological objects like M\"obius strips and Penrose triangles, and can be quantified by a nonadiabatic cyclic geometric phase which includes contributions only from the participating bands. We analytically derive a complete phase diagram with the phase boundaries of the model. We further examine the connection between the encircling of multiple EPs by complex-energy bands on parametric space and associated topology.Comment: non-Hermitian physics, topology, composite loops, Complex Zak phase, Composite Zak phase, topological invariant, M\"obius strips, Penrose triagl

Bipolar affective disorder and its impact on various aspects of marital relationship

Bipolar disorder (BD) is a severe mental disorder, which not only has negative consequences on the life of the patient, but also affects the immediate family members. As it often starts early in life, patients who get married often suffer from many negative consequences in their marital life due to the illness. This review focuses on studies which have evaluated marital rates, rate of marital failure, divorce, infertility, and procreation among patients with BD. In addition, this review evaluates the existing literature pertaining to marital adjustment, marital satisfaction, sexual dysfunction, and sexual satisfaction among patients with BD and their partners/spouses. Data suggest that very high proportion of patients with BD get married and marital rates are higher for patients with BD, when compared with those suffering from schizophrenia. In terms of divorce rates, studies suggest that patients with BD have higher rates of divorce. In terms of fertility rates, studies suggest that compared to those without the illness, the fertility rates among patients with BD are lower. In terms of marital adjustment, results are mixed with some studies suggesting poorer marital adjustment among patients and their spouses too. In terms of sexual dysfunction, studies suggest the presence of sexual dysfunction among one-third to half of the patients receiving lithium. To conclude, this review suggests that patients with BD experience multiple negative marital and sexual consequences