相关论文: Band theory in the context of the Hamilton-Jacobi …

The additional information within a Hamilton-Jacobi representation of quantum mechanics is extra, in general, to the Schr\"odinger representation. This additional information specifies the microstate of $\psi$ that is incorporated into the…

A new method for calculation of band structure has been proposed based on the Green's function theory and local sampling. Potential energy in the Hamiltonian of Schrodinger's equation is approximated with a series of sampled Dirac delta…

We describe a non-perturbative method for computing the energy band structures of one-dimensional models with general point potentials sitting at equally spaced sites. This is done thanks to a Bethe ansatz approach and the method is…

Fractional calculus has become an essential framework in geophysics, optics, and biological systems to capture long-range correlations and anomalous transport. In this article, we extend fractional calculus to explore a particle in a…

We derive the semiclassical WKB quantization condition for obtaining the energy band edges of periodic potentials. The derivation is based on an approach which is much simpler than the usual method of interpolating with linear potentials in…

In this paper we consider the continuity of the band functions and Bloch functions of the differential operators generated by the differential expressions with periodic matrix coefficients.

We study the dispersion relation of the excitations of a dilute Bose-Einstein condensate confined in a periodic optical potential and its Bloch oscillations in an accelerated frame. The problem is reduced to one-dimensionality through a…

The group theoretical treatment of bound and scattering state problems is extended to include band structure. We show that one can realize Hamiltonians with periodic potentials as dynamical symmetries, where representation theory provides…

Periodic structures are ubiquitous in quantum many-body systems and quantum field theories, ranging from lattice models, compact spaces, to topological phenomena. However, previous bootstrap studies encountered technical challenges even for…

Probability waves in the configuration space are associated with coherent solutions of the classical Liouville or Fokker-Planck equations. Distributions localized in the momentum space provide action waves, specified by the probability…

Starting from a general $N$-band Hamiltonian with weak spatial and temporal variations, we derive a low energy effective theory for transport within one or several overlapping bands. To this end, we use the Wigner representation that allows…

Quantum particle transmission through locally periodic potentials surrounded by symmetric exterior potentials is analyzed. Closed-form conditions for locating energy peaks of total transmission are derived. Floquet/Bloch energy band types…

Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of quantum mechanical problems, such as the single particle Schr\"odinger equation with an…

The band gap, a key concept in solid-state physics, is traditionally explained by the Bragg diffraction of electron waves in the periodic potential of a crystal. Although widely accepted, this framework raises fundamental issues in…

Band structure analysis is central to understanding wave propagation in periodic media; however, it becomes challenging in open systems owing to energy leakage. Photonic crystal (PhC) slabs exemplify such systems, featuring periodicity in…

Various quasi-exact solvability conditions, involving the parameters of the periodic associated Lam{\'e} potential, are shown to emerge naturally in the quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity of the…

In spatially periodic Hermitian systems, such as electronic systems in crystals, the band structure is described by the band theory in terms of the Bloch wave functions, which reproduce energy levels for large systems with open boundaries.…

We review the current status of one dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics, one can considerably enlarge the limited class of…

A class of periodic solutions of the nonlinear Schrodinger equation with non- Hermitian potentials are considered. The system may be implemented in planar nonlinear optical waveguides carrying an appropriate distribution of local gain and…

A mechanism to modify the energy band structure is proposed by considering a chain of periodic scatterers forming a linear lattice around which an external cylindrical trapping potential is applied along the chain axis. When this trapping…