Optical and transport properties in doped two-leg ladder antiferromagnet

Within the t-J model, the optical and transport properties of the doped two-leg ladder antiferromagnet are studied based on the fermion-spin theory. It is shown that the optical and transport properties of the doped two-leg ladder antiferromagnet are mainly governed by the holon scattering. The low energy peak in the optical conductivity is located at a finite energy, while the resistivity exhibits a crossover from the high temperature metallic-like behavior to the low temperature insulating-like behavior, which are consistent with the experiments.Comment: 13 pages, 5 figures, accepted for publication in Phys. Rev. B65 (2002) (April 15 issue

Uniqueness of nontrivially complete monotonicity for a class of functions involving polygamma functions

For $m,n\in\mathbb{N}$, let $f_{m,n}(x)=\bigr[\psi^{(m)}(x)\bigl]^2+\psi^{(n)}(x)$ on $(0,\infty)$. In the present paper, we prove using two methods that, among all $f_{m,n}(x)$ for $m,n\in\mathbb{N}$, only $f_{1,2}(x)$ is nontrivially completely monotonic on $(0,\infty)$. Accurately, the functions $f_{1,2}(x)$ and $f_{m,2n-1}(x)$ are completely monotonic on $(0,\infty)$, but the functions $f_{m,2n}(x)$ for $(m,n)\ne(1,1)$ are not monotonic and does not keep the same sign on $(0,\infty)$.Comment: 9 page

Chiral Rings and Phases of Supersymmetric Gauge Theories

We solve for the expectation values of chiral operators in supersymmetric U(N) gauge theories with matter in the adjoint, fundamental and anti-fundamental representations. A simple geometric picture emerges involving a description by a meromorphic one-form on a Riemann surface. The equations of motion are equivalent to a condition on the integrality of periods of this form. The solution indicates that all semiclassical phases with the same number of U(1) factors are continuously connected.Comment: 55 page

Statistical Mechanical Theory of a Closed Oscillating Universe

Based on Newton's laws reformulated in the Hamiltonian dynamics combined with statistical mechanics, we formulate a statistical mechanical theory supporting the hypothesis of a closed oscillating universe. We find that the behaviour of the universe as a whole can be represented by a free entropic oscillator whose lifespan is nonhomogeneous, thus implying that time is shorter or longer according to the state of the universe itself given through its entropy. We conclude that time reduces to the entropy production of the universe and that a nonzero entropy production means that local fluctuations could exist giving rise to the appearance of masses and to the curvature of the space

Analytical results on quantum interference and magnetoconductance for strongly localized electrons in a magnetic field: Exact summation of forward-scattering paths

We study quantum interference effects on the transition strength for strongly localized electrons hopping on 2D square and 3D cubic lattices in the presence of a magnetic field B. These effects arise from the interference between phase factors associated with different electron paths connecting two distinct sites. For electrons confined on a square lattice, with and without disorder, we obtain closed-form expressions for the tunneling probability, which determines the conductivity, between two arbitrary sites by exactly summing the corresponding phase factors of all forward-scattering paths connecting them. An analytic field-dependent expression, valid in any dimension, for the magnetoconductance (MC) is derived. A positive MC is clearly observed when turning on the magnetic field. In 2D, when the strength of B reaches a certain value, which is inversely proportional to twice the hopping length, the MC is increased by a factor of two compared to that at zero field. We also investigate transport on the much less-studied and experimentally important 3D cubic lattice case, where it is shown how the interference patterns and the small-field behavior of the MC vary according to the orientation of B. The effect on the low-flux MC due to the randomness of the angles between the hopping direction and the orientation of B is also examined analytically.Comment: 24 pages, RevTeX, 8 figures include

A quadtree-polygon-based scaled boundary finite element method for image-based mesoscale fracture modelling in concrete

A quadtree-polygon scaled boundary finite element-based approach for image-based modelling of concrete fracture at the mesoscale is developed. Digital images representing the two-phase mesostructure of concrete, which comprises of coarse aggregates and mortar are either generated using a take-and-place algorithm with a user-defined aggregate volume ratio or obtained from X-ray computed tomography as an input. The digital images are automatically discretised for analysis by applying a balanced quadtree decomposition in combination with a smoothing operation. The scaled boundary finite element method is applied to model the constituents in the concrete mesostructure. A quadtree formulation within the framework of the scaled boundary finite element method is advantageous in that the displacement compatibility between the cells are automatically preserved even in the presence of hanging nodes. Moreover, the geometric flexibility of the scaled boundary finite element method facilitates the use of arbitrary sided polygons, allowing better representation of the aggregate boundaries. The computational burden is significantly reduced as there are only finite number of cell types in a balanced quadtree mesh. The cells in the mesh are connected to each other using cohesive interface elements with appropriate softening laws to model the fracture of the mesostructure. Parametric studies are carried out on concrete specimens subjected to uniaxial tension to investigate the effects of various parameters e.g. aggregate size distribution, porosity and aggregate volume ratio on the fracture of concrete at the meso-scale. Mesoscale fracture of concrete specimens obtained from X-ray computed tomography scans are carried out to demonstrate its feasibility

Electromotive forces and the Meissner effect puzzle

In a voltaic cell, positive (negative) ions flow from the low (high) potential electrode to the high (low) potential electrode, driven by an `electromotive force' which points in opposite direction and overcomes the electric force. Similarly in a superconductor charge flows in direction opposite to that dictated by the Faraday electric field as the magnetic field is expelled in the Meissner effect. The puzzle is the same in both cases: what drives electric charges against electromagnetic forces? I propose that the answer is also the same in both cases: kinetic energy lowering, or `quantum pressure'

Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains

Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-reversed. The effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process, and vice-versa, revealing that the distributions of fluctuations in universes in which time moves forward and backward are related. As an additional result, the asymptotic time-averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics

Symmetry and topology in antiferromagnetic spintronics

Antiferromagnetic spintronics focuses on investigating and using antiferromagnets as active elements in spintronics structures. Last decade advances in relativistic spintronics led to the discovery of the staggered, current-induced field in antiferromagnets. The corresponding N\'{e}el spin-orbit torque allowed for efficient electrical switching of antiferromagnetic moments and, in combination with electrical readout, for the demonstration of experimental antiferromagnetic memory devices. In parallel, the anomalous Hall effect was predicted and subsequently observed in antiferromagnets. A new field of spintronics based on antiferromagnets has emerged. We will focus here on the introduction into the most significant discoveries which shaped the field together with a more recent spin-off focusing on combining antiferromagnetic spintronics with topological effects, such as antiferromagnetic topological semimetals and insulators, and the interplay of antiferromagnetism, topology, and superconductivity in heterostructures.Comment: Book chapte