Stability of ferromagnetism in the Hubbard model on the kagom\'e lattice

The Hubbard model on the kagom\'e lattice has highly degenerate ground states (the flat lowest band) in the corresponding single-electron problem and exhibits the so-called flat-band ferromagnetism in the many-electron ground states as was found by Mielke. Here we study the model obtained by adding extra hopping terms to the above model. The lowest single-electron band becomes dispersive, and there is no band gap between the lowest band and the other band. We prove that, at half-filling of the lowest band, the ground states of this perturbed model remain saturated ferromagnetic if the lowest band is nearly flat.Comment: 4 pages, 1 figur

Flat-Bands on Partial Line Graphs -- Systematic Method for Generating Flat-Band Lattice Structures

We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied to two- and three-dimensional systems. We show examples of partial line graphs of square and cubic lattices. The method is useful in providing a guideline for synthesizing materials with flat energy bands, since the tight-binding models on the partial line graphs provide us a large room for modification, maintaining the flat energy dispersions.Comment: 9 pages, 4 figure

An Information--Theoretic Equality Implying the Jarzynski Relation

We derive a general information-theoretic equality for a system undergoing two projective measurements separated by a general temporal evolution. The equality implies the non-negativity of the mutual information between the measurement outcomes of the earlier and later projective measurements. We show that it also contains the Jarzynski relation between the average exponential of the thermodynamical work and the exponential of the difference between the initial and final free energy. Our result elucidates the information-theoretic underpinning of thermodynamics and explains why the Jarzynski relation holds identically both quantumly as well as classically.Comment: 2 pages, no figure

Magnetic field effects on two-dimensional Kagome lattices

Magnetic field effects on single-particle energy bands (Hofstadter butterfly), Hall conductance, flat-band ferromagnetism, and magnetoresistance of two-dimensional Kagome lattices are studied. The flat-band ferromagnetism is shown to be broken as the flat-band has finite dispersion in the magnetic field. A metal-insulator transition induced by the magnetic field (giant negative magnetoresistance) is predicted. In the half-filled flat band, the ferromagnetic-paramagnetic transition and the metal-insulator one occur simultaneously at a magnetic field for strongly interacting electrons. All of the important magnetic fields effects should be observable in mesoscopic systems such as quantum dot superlattices.Comment: 10 pages, 4 figures, and 1 tabl

Microscopic analysis of the microscopic reversibility in quantum systems

We investigate the robustness of the microscopic reversibility in open quantum systems which is discussed by Monnai [arXiv:1106.1982 (2011)]. We derive an exact relation between the forward transition probability and the reversed transition probability in the case of a general measurement basis. We show that the microscopic reversibility acquires some corrections in general and discuss the physical meaning of the corrections. Under certain processes, some of the correction terms vanish and we numerically confirmed that the remaining correction term becomes negligible; the microscopic reversibility almost holds even when the local system cannot be regarded as macroscopic.Comment: 12 pages, 10 figure

The two dimensional Hubbard model:a theoretical tool for molecular electronics

When speaking about molecular electronics, the obvious question which occurs is how does one study it theoretically. The simplest theoretical model suitable for application in molecular electronics is the two dimensional Hubbard model. The aim of the present paper is to introduce this model, and give some examples of the systems which it can describe. After a short mathematically oriented discussion, it will be shown how to calculate the electrical conductivity of a particular planar system: a rectangular lattice with mutually independent conductivities along the two axes,but without using the 2D Hamiltonian. This system could find applications in high Tc studies. It will finally be shown that the electrical conductivity of graphene can be determined not by using the full formalism of the $2D$ Hubbard model, but by a slight reformulation of the Hamiltonian of the 1D Hubbard modelComment: Lecture given at the 16 Int.School of Cond.Matt.Physics,August 29.,-September 3 2010.,Varna (Bulgaria

Fluctuation theorem for currents in open quantum systems

A quantum-mechanical framework is set up to describe the full counting statistics of particles flowing between reservoirs in an open system under time-dependent driving. A symmetry relation is obtained which is the consequence of microreversibility for the probability of the nonequilibrium work and the transfer of particles and energy between the reservoirs. In some appropriate long-time limit, the symmetry relation leads to a steady-state quantum fluctuation theorem for the currents between the reservoirs. On this basis, relationships are deduced which extend the Onsager-Casimir reciprocity relations to the nonlinear response coefficients.Comment: 19 page

On the Quantum Jarzynski Identity

In this note, we will discuss how to compactly express and prove the Jarzynski identity for an open quantum system with dissipative dynamics. We will avoid explicitly measuring the work directly, which is tantamount to continuously monitoring the system, and instead measure the heat flow from the environment. We represent the measurement of heat flow with Hermitian map superoperators that act on the system density matrix. Hermitian maps provide a convenient and compact representation of sequential measurement and correlation functions.Comment: 4 page

The N-end rule pathway controls multiple functions during Arabidopsis shoot and leaf development

The ubiquitin-dependent N-end rule pathway relates the in vivo half-life of a protein to the identity of its N-terminal residue. This proteolytic system is present in all organisms examined and has been shown to have a multitude of functions in animals and fungi. In plants, however, the functional understanding of the N-end rule pathway is only beginning. The N-end rule has a hierarchic structure. Destabilizing activity of N-terminal Asp, Glu, and (oxidized) Cys requires their conjugation to Arg by an arginyl–tRNA–protein transferase (R-transferase). The resulting N-terminal Arg is recognized by the pathway's E3 ubiquitin ligases, called “N-recognins.” Here, we show that the Arabidopsis R-transferases AtATE1 and AtATE2 regulate various aspects of leaf and shoot development. We also show that the previously identified N-recognin PROTEOLYSIS6 (PRT6) mediates these R-transferase-dependent activities. We further demonstrate that the arginylation branch of the N-end rule pathway plays a role in repressing the meristem-promoting BREVIPEDICELLUS (BP) gene in developing leaves. BP expression is known to be excluded from Arabidopsis leaves by the activities of the ASYMMETRIC LEAVES1 (AS1) transcription factor complex and the phytohormone auxin. Our results suggest that AtATE1 and AtATE2 act redundantly with AS1, but independently of auxin, in the control of leaf development

Metallic ferromagnetism: Progress in our understanding of an old strong-coupling problem

Metallic ferromagnetism is in general an intermediate to strong coupling phenomenon. Since there do not exist systematic analytic methods to investigate such types of problems, the microscopic origin of metallic ferromagnetism is still not sufficiently understood. However, during the last two or three years remarkable progress was made in this field: It is now certain that even in the one-band Hubbard model metallic ferromagnetism is stable in dimensions $d=1,$ 2, and $\infty$ on regular lattices and at intermediate values of the interaction $U$ and density $n$. In this paper the basic questions and recent insights regarding the microscopic conditions favoring metallic ferromagnetism in this model are reviewed. These findings are contrasted with the results for the orbitally degenerate case.Comment: 16 pages, 13 figures, latex using vieweg.sty (enclosed); typos corrected; to appear in "Advances in Solid State Physics", Vol. 3