Spectrum Of Hamiltonian Research Articles

First-principles study of rectifying and switching behavior for different contact positions between sulfur-terminated armchair graphene nanoribbons junctions

Transport properties of armchair graphene nanoribbon junctions with different widths are investigated on the zigzag edges terminated with sulfur atoms. The first-principles calculations based on the non-equilibrium Green's functions together with the density-functional theory show that their characteristics display obvious rectifying performance and switching behavior which are sensitive to the contact points and external activation. The analysis of the Mulliken charge distribution and projected Hamiltonian energy spectrum provides an inside view of the electronic structure of the ground state. The non-equilibrium states analysis, incorporating the density of states and projected density of states as well as the evolutions of frontier orbitals under various external biases, reveals that the intrinsic origin of the different rectifying performances is a result of the asymmetric movement of conducting states and contributing orbitals.

Some Remarks on the Spectrum of the Magnetic Stark Hamiltonians

The main purpose of this note is to study spectral properties of the Stark magnetic Hamiltonian : , on the Hilbert space L 2 (R 2 ). We show that if the potential V satisfies some mild regularity conditions and is sufficiently decaying at infinity, then the operator H(μ, ϵ) has possibly at most a finite number of eigenvalues.

A new approach to the $N$-particle problem in QM

In this paper the old problem of determining the discrete spectrum of a multi-particle Hamiltonian is reconsidered. The aim is to bring a fermionic Hamiltonian for arbitrary numbers $N$ of particles by analytical means into a shape such that modern numerical methods can successfully be applied. For this purpose the Cook-Schroeck Formalism is taken as starting point. This includes the use of the occupation number representation. It is shown that the $N$-particle Hamiltonian is determined in a canonical way by a fictional 2-particle Hamiltonian. A special approximation of this 2-particle operator delivers an approximation of the $N$-particle Hamiltonian, which is the orthogonal sum of finite dimensional operators. A complete classification of the matrices of these operators is given. Finally the method presented here is formulated as a work program for practical applications. The connection with other methods for solving the same problem is discussed.

A Note on the Spectrum of a Two-particle Rashba Hamiltonian

In a series of recent papers it was shown that, when the attractive s-wave interaction is dominant, the spin-orbit coupled fermions form a bound state. Attributed to a convenient momentum representation, it became a common condition of agreement to express the bound state as a function of the center-of-mass momentum Q. In this letter we prove that the bound state of Rashba fermions does not depend on the chosen representation. That is, all the states characterized by nonzero Q fail to obey the translation symmetry.

Perspective: Relativistic Hamiltonians

Under the no‐photon approximation, an effective quantum electrodynamics (QED) Hamiltonian can be constructed based solely on charge conjugation symmetry. It serves as the basis not only for the emerging field of “molecular QED” but also for various approximate Hamiltonians, including the standard no‐pair ones. The whole spectrum of relativistic Hamiltonians is hence completed. © 2013 Wiley Periodicals, Inc.

Adiabatic projection method for scattering and reactions on the lattice

We demonstrate and test the adiabatic projection method, a general new framework for calculating scattering and reactions on the lattice. The method is based upon calculating a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time. As a detailed example we calculate the adiabatic two-body Hamiltonian for elastic fermion-dimer scattering in lattice effective field theory. Our calculation corresponds to neutron-deuteron scattering in the spin-quartet channel at leading order in pionless effective field theory. We show that the spectrum of the adiabatic Hamiltonian reproduces the spectrum of the original Hamiltonian below the inelastic threshold to arbitrary accuracy. We also show that the calculated s -wave phase shift reproduces the known exact result in the continuum and infinite-volume limits. When extended to more than one scattering channel, the adiabatic projection method can be used to calculate inelastic reactions on the lattice in future work.

Band structure of the spectra of Hamiltonians of regular polynucleotide duplexes

We calculate the band structure of the spectra of Hamiltonians of regular DNA duplexes and show that in single-stranded periodic polynucleotides whose period is determined by the number m of nucleotides in an elementary cell, the spectrum consists of m nonintersecting energy bands. In DNA duplexes, the number of energy bands is equal to 2m, and the bands can intersect. Discrete energy levels can be present in forbidden bands in the case of (semi)bounded chains or duplexes.

Hermitian Hamiltonian equivalent to a given non-Hermitian one: manifestation of spectral singularity

One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equivalent to the given non-Hermitian one is found. As a result, the corresponding scattering matrix and cross section are given explicitly. It is demonstrated that the possible presence of a spectral singularity in the spectrum of the non-Hermitian Hamiltonian may be detected as a resonance in the scattering cross section of its Hermitian counterpart. Nevertheless, just at the singular point, the equivalent Hermitian Hamiltonian becomes undetermined.

A note on the switching adiabatic theorem

We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey class Gα as a function of time, and we show that the error in adiabatic approximation remains small for running times of order g−2 |ln g |6α. Here g denotes the minimal spectral gap between the eigenvalue(s) of interest and the rest of the spectrum of the instantaneous Hamiltonian.

Scale Invariance, Self Similarity and Critical Behavior in Classical and Quantum Systems

Symmetry and self-affinity or scale invariance are related concepts. We explore the fractal properties of fluctuations in dynamical systems, using some of the available tools in the context of time series analysis. We carry out a power spectrum study in the Fourier domain, the method of detrended fluctuation analysis and the investigation of autocorrelation function behavior. Our study focuses on two particular examples, the logistic module-1 map, which displays properties of classical dynamical systems, and the excitation spectrum of a schematic shell-model Hamiltonian, which is a simple system exhibiting quantum chaos.

Spin Transport in Be Edge-Doped Graphene Nanoribbon

We report an atomistic simulation of spin dependent charge transport in zigzag graphene nanoribbons with 4 zigzag chains doped by a Beryllium atom on one edge. The spin dependent density functional theory with norm-conserving atomic basis set is employed to describe the system and the current versus voltage behavior is calculated by the nonequilibrium Green's function method for quantum transport. The Be impurity atom suppresses the local magnetization near the edge and the transmitted charge current becomes spin polarized accordingly. Both spin-up and spin-down transmission spectra are modified significantly but in different ways. Distinguished from the previous doping results of other impurity elements, here we observe negative differential resistance for only one of the spins in the nonlinear transport regime below bias 1.5 V. Molecular projected Hamiltonian energy spectrum near the impurity shows that the impurity removes the energy degeneracy of spin in perfect ribbon. The current versus voltage shows semiconductor behavior with fluctuating spin polarization of amplitude up to 37%.

GENERALIZED COHERENT STATES APPROACH TO DEFORMATION QUANTIZATION

Generalized (f)-coherent state approach in deformation quantization framework is investigated by using a *-eigenvalue equation. For this purpose we introduce a new Moyal star product called f-star product, so that by using this *f-eigenvalue equation one can obtain exactly the spectrum of a general Hamiltonian of a deformed system. Eventually the method is supported with some examples.

Topological and entanglement properties of resonating valence bond wave functions

We examine in details the connections between topological and entanglement properties of short-range resonating valence bond (RVB) wave functions using Projected Entangled Pair States (PEPS) on kagome and square lattices on (quasi-)infinite cylinders with generalized boundary conditions (and perimeters with up to 20 lattice spacings). Making use of disconnected topological sectors in the space of dimer lattice coverings, we explicitly derive (orthogonal) "minimally entangled" PEPS RVB states. For the kagome lattice, we obtain, using the quantum Heisenberg antiferromagnet as a reference model, the finite size scaling of the energy separations between these states. In particular, we extract two separate (vanishing) energy scales corresponding (i) to insert a vison line between the two ends of the cylinder and (ii) to pull out and freeze a spin at either end. We also investigate the relations between bulk and boundary properties and show that, for a bipartition of the cylinder, the boundary Hamiltonian defined on the edge can be written as a product of a highly non-local projector with an emergent (local) su(2)-invariant one-dimensional (superfluid) t--J Hamiltonian, which arises due to the symmetry properties of the auxiliary spins at the edge. This multiplicative structure, a consequence of the disconnected topological sectors in the space of dimer lattice coverings, is characteristic of the topological nature of the states. For minimally entangled RVB states, it is shown that the entanglement spectrum, which reflects the properties of the edge modes, is a subset (half for kagome RVB) of the spectrum of the local Hamiltonian, providing e.g. a simple argument on the origin of the topological entanglement entropy S0=-ln 2 of Z2 spin liquids. We propose to use these features to probe topological phases in microscopic Hamiltonians and some results are compared to existing DMRG data.

Hall quantum Hamiltonians and electric 2D-curvature

Received Abstract. For the Dirac 2D-operator in a constant magnetic field with perturbing electric potential, we derive Hamiltonians describing the quantum quasiparticles (Larmor vortices) at Landau levels. The discrete spectrum of this Hall-effect quantum Hamiltonian can be computed to all orders of the semiclassical approximation by a deformed Planck-type quan- tization condition on the 2D-plane; the standard magnetic (symplectic) form on the plane is corrected by an "electric curvature" determined via derivatives of the electric field. The electric curvature does not depend on the magnitude of the electric field and vanishes for homogeneous fields (i.e., for the canonical Hall effect). This curvature can be treated as an effective magnetic charge of the inhomogeneous Hall 2D-nanosystem.

The hamiltonian numbers in digraphs

In the paper, we study the hamiltonian numbers in digraphs. A hamiltonian walk of a digraph D is a closed spanning directed walk with minimum length in D. The length of a hamiltonian walk of a digraph D is called the hamiltonian number of D, denoted h(D). We prove that if a digraph D of order n is strongly connected, then \(n\leq h(D)\leq\lfloor\frac{(n+1)^{2}}{4} \rfloor\), and hence characterize the strongly connected digraphs of order n with hamiltonian number \(\lfloor\frac{(n+1)^{2}}{4} \rfloor\). In addition, we show that for each k with \(4\leq n\leq k\leq\lfloor \frac{(n+1)^{2}}{4} \rfloor\), there exists a digraph with order n and hamiltonian number k. Furthermore, we also study the hamiltonian spectra of graphs.

Wentzel-Kramers-Brillouin analysis ofPT-symmetric Sturm-Liouville problems

In a previous paper it was shown that a one-turning-point WKB approximation gives an accurate picture of the spectrum of certain non-Hermitian PT-symmetric Hamiltonians on a finite interval with Dirichlet boundary conditions. Potentials to which this analysis applies include the linear potential $V=igx$ and the sinusoidal potential $V=ig\sin(\alpha x)$. However, the one-turning-point analysis fails to give the full structure of the spectrum for the cubic potential $V=igx^3$, and in particular it fails to reproduce the critical points at which two real eigenvalues merge and become a complex-conjugate pair. The present paper extends the method to cases where the WKB path goes through a {\it pair} of turning points. The extended method gives an extremely accurate approximation to the spectrum of $V=igx^3$, and more generally it works for potentials of the form $V=igx^{2N+1}$. When applied to potentials with half-integral powers of $x$, the method again works well for one sign of the coupling, namely that for which the turning points lie on the first sheet in the lower-half plane.

Floquet analysis of the modulated two-mode Bose-Hubbard model

We study the tunneling dynamics in a time-periodically modulated two-mode Bose-Hubbard model using Floquet theory. We consider situations where the system is in the self-trapping regime and either the tunneling amplitude, the interaction strength, or the energy difference between the modes is modulated. In the former two cases, the tunneling is enhanced in a wide range of modulation frequencies, while in the latter case the resonance is narrow. We explain this difference with the help of Floquet analysis. If the modulation amplitude is weak, the locations of the resonances can be found using the spectrum of the non-modulated Hamiltonian. Furthermore, we use Floquet analysis to explain the coherent destruction of tunneling (CDT) occurring in a large-amplitude modulated system. Finally, we present two ways to create a NOON state (a superposition of $N$ particles in mode 1 with zero particles in mode 2 and vice versa). One is based on a coherent oscillation caused by detuning from a partial CDT. The other makes use of an adiabatic variation of the modulation frequency. This results in a Landau-Zener type of transition between the ground state and a NOON-like state.

Multiplicity function for tensor powers of modules of the A n algebra

We consider the decomposition of the pth tensor power of the module \(L^{\omega _1 }\) over the algebra An into irreducible modules, \((L^{\omega _1 } )^{ \otimes p} = \sum\nolimits_v {m(v,p)L^v }\). This problem occurs, for example, in finding the spectrum of an invariant Hamiltonian of a spin chain with p nodes. To solve the problem, we propose using the Weyl symmetry properties. For constructing the coefficients m(ν, p) as functions of p, we develop an algorithm applicable to powers of an arbitrary module. We explicitly write an expression for the multiplicities m(ν, p) in the decomposition of powers of the first fundamental module of sl(n+1). Based on the obtained results, we find new properties of systems of orthogonal polynomials (multivariate Chebyshev polynomials). Our algorithm can also be applied to tensor powers of modules of other simple Lie algebras.

Upper Bound for the Bethe–Sommerfeld Threshold and the Spectrum of the Poisson Random Hamiltonian in Two Dimensions

We consider the Schrodinger operator on \({\mathbb{R}^2}\) with a locally square-integrable periodic potential V and give an upper bound for the Bethe–Sommerfeld threshold (the minimal energy above which no spectral gaps occur) with respect to the square-integrable norm of V on a fundamental domain, provided that V is small. As an application, we prove the spectrum of the two-dimensional Schrodinger operator with the Poisson type random potential almost surely equals the positive real axis or the whole real axis, according as the negative part of the single-site potential equals zero or not. The latter result completes the missing part of the result by Ando et al. (Ann Henri Poincare 7:145–160, 2006).

Solvability of the two-photon Rabi Hamiltonian

Exact spectrum of the two-photon Rabi Hamiltonian is found, proceeding in full analogy with the solution of standard (one-photon) Rabi Hamiltonian, published by Braak in Phys. Rev. Lett. 107, 100401 (2011). The Hamiltonian is rewritten as a set of two differential equations. Symmetries that get hidden after further treatment are found. One can plainly see, how the Hilbert space splits into four disjunct subspaces, categorized by four values of the symmetry parameter $c=\pm1,\pm i$. There were only two values $\pm1$ for the standard Rabi model. Four analytic functions are introduced by a recurrence scheme for the coefficients of their series expansion. All their roots yield the complete spectrum of the Hamiltonian. Eigenstates in Bargmann space are also at disposal.