相关论文: Topology, Quasiperiodic functions and the Transpor…

We consider Novikov problem of the classification of level curves of quasiperiodic functions on the plane and its connection with the conductivity of two-dimensional electron gas in the presence of both orthogonal magnetic field and the…

While quasiperiodic functions in one variable appeared in applications since Eighteen hundreds, for example in connection with the trajectories of mechanical systems with 2n degress of freedom having n commuting first integrals, the first…

The paper is devoted to the questions connected with the investigation of the S.P. Novikov problem of the description of the geometry of level lines of quasiperiodic functions on a plane with different numbers of quasiperiods. We consider…

The article describes a topological theory of quasiperiodic functions on the plane. The development of this theory was started (in different terminology) by the Moscow topology group in early 1980s. It was motivated by the needs of solid…

Topology of levels of the quasiperiodic functions with m=n+2 periods on the plane is studied. For the case of functions with m=4 periods full description is obtained for the open everywhere dense family of functions. This problem is…

The present article proposes a review of the most recent results obtained in the study of Novikov's problem on the description of the geometry of the level lines of quasi-periodic functions in the plane. Most of the paper is devoted to the…

This is a survey article dedicated to the study of topological quantities in theory of normal metals discovered in the works of the authors during the last years. Our results are based on the theory of dynamical systems on Fermi surfaces.…

Topological phases of matter have sparked an immense amount of activity in recent decades. Topological materials are classified by topological invariants that act as a non-local order parameter for any symmetry and condition. As a result,…

Hystory of topology is discussed uncluding the Golden Age Period (1950-1970), the Period of Decay (1970-1980) and the Period of Recovery in 80s and 90s based on the ideas borrowed from physics community. In the second part recent result of…

This paper is devoted to topological phenomena in normal metals with rather complicated Fermi surface. The results of the article are based on the deep topological theorems concerning the geometry of non-compact plane sections of level…

It has recently been argued that individual 1D quasicrystals can be ascribed 2D topological quantum numbers and a corresponding set of topologically protected edge modes. Here, we demonstrate the equivalence of such 1D quasicrystals to a…

Thermal transport is a fundamental mechanism of energy transfer process quite distinct from wave propagation phenomena. It can be manipulated well beyond the possibilities offered by natural materials with a new generation of artificial…

This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…

We consider here quasiperiodic potentials on the plane, which can serve as a "transitional link" between ordered (periodic) and chaotic (random) potentials. As can be shown, in almost any family of quasiperiodic potentials depending on a…

Topological transport is determined by global properties of physical media where it occurs and is characterized by quantized amounts of adiabatically transported quantities. Discovered for periodic potentials it was also explored in…

Quasiperiodic systems extend the concept of the Anderson transition to quasi-random and low-dimensional realms and have garnered widespread attention. Here, we propose the asymptotic quasiperiodic two-dimensional systems characterized by a…

The paper is devoted to the applications of the theory of dynamical systems to the theory of transport phenomena in metals in the presence of strong magnetic fields. More precisely, we consider the connection between the geometry of the…

Using a combination of numerically exact and renormalization-group techniques we study the nonequilibrium transport of electrons in an one-dimensional interacting system subject to a quasiperiodic potential. For this purpose we calculate…

The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory - general relativity. The inability to define complete initial data consistently and independently of future measurements,…

Topological effects typically discussed in the context of quantum physics are emerging as one of the central paradigms of physics. Here, we demonstrate the role of topology in energy transport through dimerized micro- and nano-mechanical…