Related papers: A continuum limit for the Kronig-Penney model
Finite length of a one channel wire results in crossover from a Tomonaga-Luttinger to Fermi liquid behavior with lowering energy scale. In condition that voltage drop $(V)$ mostly occurs across a tunnel barrier inside the wire we found…
We analyze the basic cosmological effects of a population of timelike boundaries -- a form of nontrivial spacetime topology -- containing a boundary layer of quantum stress energy. This accumulation of vacuum fluctuations of quantum fields…
We numerically study the distribution function of the conductance (transmission) in the one-dimensional tight-binding Anderson and periodic-on-average superlattice models in the region of fluctuation states where single parameter scaling is…
The phenomenon of wavepacket diffraction in space and time is investigated numerically and analytically, for a one-dimensional array of equally spaced finite-depth wells. Theoretical predictions for the lattice at long times and at low…
We study directed last-passage percolation on the planar square lattice whose weights have general distributions, or equivalently, queues in series with general service distributions. Each row of the last passage model has its own randomly…
Transmission of electrons across a rectangular barrier of IV-VI semiconductor compounds is considered. Conduction electrons arrive at the barrier and are reflected or transmitted through it depending on the relative values of the barrier…
In this work, a one-dimensional model of crystalline solids based on the Dirac comb limit of the Kronig-Penney model is considered. From the wave functions of the valence electrons, we calculate a statistical measure of complexity and the…
We present the first experimental investigation of modulational instability in a layered Kerr medium. The particularly interesting and appealing feature of our configuration, consisting of alternating glass-air layers, is the…
The transmission of fermions of mass m and energy E through an electrostatic potential barrier of rectangular shape (i.e. supporting an infinite electric field), of height U> E + m - due to the many-body nature of the Dirac equation…
We present a unified framework, with quantitative estimates, for deterministic interacting particle systems whose pairwise interactions may depend on heterogeneous labels. Heterogeneity is kept at every level by adding a frozen label…
Quantum physics allows for unconditionally secure communication through insecure communication channels. The achievable rates of quantum-secured communication are fundamentally limited by the laws of quantum physics and in particular by the…
Discoveries of fundamental limits for the rates of physical processes, from the speed of light to the Lieb-Robinson bound for information propagation, often lead to breakthroughs in the our understanding of the underlying physics. Here we…
We study correlated quantum wires subject to harmonic modulation of the onsite-potential concentrating on the limit of large times, where the response of the system has synchronized with the drive. We identify the ratio…
A finit periodic $\delta-\delta'$ comb was solved by the help of both classical approach based on a direct solving of a Sr\"{odinger} equation and a quantum wave impedance method. It was demonstrated that the violation of a periodicity…
Convergence of solutions to a partially diffusive chemotaxis system with indirect signal production and phenotype switching is shown in a two-dimensional setting when the switching rate increases to infinity, thereby providing a rigorous…
The delta function potential is a simple model of zero-range contact interaction in one dimension. The Kronig-Penney model is a one-dimensional periodic array of delta functions that models the energy bands in a crystal. Here we investigate…
Information must take up space, must weigh, and its flux must be limited. Quantum limits on communication and information storage leading to these conclusions are here described. Quantum channel capacity theory is reviewed for both steady…
The scaling limit of the less than half filled attractive Hubbard chain is studied. This is a continuum limit in which the particle number per lattice site, n, is kept finite (0<n<1) while adjusting the interaction and bandwidth in a such…
We study the transport through two impurities or ``barriers'' in a one-dimensional quantum wire, taking into account the long-range $\frac1r$ Coulomb interactions. We compute the temperature-dependent conductance $G(T)$ of this system.…
We investigate the Peak-Power Limited (PPL) Additive White Gaussian Noise (AWGN) channels in which the signal is band-limited, and its instantaneous power cannot exceed the power P. This model is relevant to many communication systems;…