Related papers: Ballistic Transport for Periodic Jacobi Operators …
We consider a periodic problem for the motion of a charged particle in a magnetic field. Introducing a notion of Ricci curvature for such Lagrangian systems and using the methods of the calculus of variations in the large, we prove the…
Jacobi elliptic functions are flexible functions that appear in a variety of problems in physics and engineering. We introduce and describe important features of these functions and present a physical example from classical mechanics where…
The magneto-resistance of antidot lattices shows pronounced peaks, which became a hallmark of ballistic electron transport. While most studies agree that they reflect the interplay of regular and chaotic motion in the quasi-classical…
Transport properties of particles and waves in spatially periodic structures that are driven by external time-dependent forces manifestly depend on the space-time symmetries of the corresponding equations of motion. A systematic analysis of…
We present in this work a proof of the exponential dichotomy for dynamically defined matrix-valued Jacobi operators in $(\mathbb{C}^{l})^{\mathbb{Z}}$, given for each $\omega \in \Omega$ by the law $[H_{\omega} \textbf{u}]_{n} := D(T^{n -…
We consider periodic Jacobi operators and obtain upper and lower estimates on the sizes of the spectral bands. Our proofs are based on estimates on the logarithmic capacities and connections between the Chebyshev polynomials and logarithmic…
We investigate the effect of periodic driving by an external field on systems with attractive pairing interactions. These include spin systems (like the ferromagnetic XXZ model) as well as ultracold fermionic atoms described by the…
We recall criteria on the spectrum of Jacobi matrices such that the corresponding isospectral torus consists of periodic operators. Motivated by those known results for Jacobi matrices, we define a new class of operators called GMP…
Using the methods of moving frames, we study real hypersurfaces in complex projective space CP^2 and complex hyperbolic space CH^2 whose structure Jacobi operator has various special properties. Our results complement work of several other…
In this paper we study transitivity of partially hyperbolic endomorphisms of the two torus whose action in the first homology has two integer eigenvalues of moduli greater than one. We prove that if the Jacobian is everywhere greater than…
In this note we prove a Birkhoff type transitivity theorem for continuous maps acting on non-separable completely metrizable spaces and we give some applications for dynamics of bounded linear operators acting on complex Fr\'{e}chet spaces.…
We prove analytically that both fermionic and bosonic uniform d-dimensional lattices can be reduced to a set of independent one-dimensional modes. This reduction leads to the conclusion that the dynamics in uniform fermionic and bosonic…
We characterize Riemannian manifolds of constant sectional curvature in terms of commutation properties of their Jacobi operators.
We study the biased random walk in positive random conductances on $\mathbb {Z}^d$. This walk is transient in the direction of the bias. Our main result is that the random walk is ballistic if, and only if, the conductances have finite…
We prove a partial result concerning the long-standing problem on limit periodicity of the Jacobi matrix associated with the balanced measure on the Julia set of an expending polynomial. Besides this, connections of the problem with the…
In this paper we use Jacobi fields to describe the motion of a charged particle in the classical gravitational, electromagnetic, and Yang-Mills fields.
Ballistic transport of electrons through a quantum wire with a constriction is studied in terms of Bohm's interpretation of quantum mechanics, in which the concept of a particle orbit is permitted. The classical bouncing ball trajectories,…
We develop direct and inverse scattering theory for Jacobi operators which are short range perturbations of quasi-periodic finite-gap operators. We show existence of transformation operators, investigate their properties, derive the…
We investigate the nonequilibrium dynamics of classical particles in a driven quasiperiodic lattice based on the Fibonacci sequence. An intricate transient dynamics of extraordinarily long ballistic flights at distinct velocities is found.…
Bidirectional variants of stochastic many particle models for transport by molecular motors show a strong tendency to form macroscopic clusters on static lattices. Inspired by the fact that the microscopic tracks for molecular motors are…