Quantization Of Energy Spectrum Research Articles

Hole-majority condition and magnetic field dependence of the electron/hole density and magnetization in a bismuth thin film

The electrons and holes in a bismuth thin film placed in a transverse magnetic field assume three-dimensionally quantized energy spectra. Peculiar magnetic field dependence of the carrier density and magnetization has been re-calculated using the hole-majority condition, replacing the conventional charge-neutrality condition. Some of the new results seem to be physically significant.

Vibrational Energy-Spectra and Infrared Absorptionof α-Helical Protein Molecules

The quantum energy spectra, including high excited states, ofvibrational amide-I or of intramolecular excitations inα-helical protein molecules, are calculated by the discretenonlinear Schrödinger equation together with the parametersappropriate to the systems. The distribution of energy levels obtainedis basically consistent with the experimental values obtained byinfrared absorption and Raman scattering. Utilizing the energy spectrawe explain the laser Raman spectrum from metabolically activeescherichia coli and we present some further features of the infraredabsorption of the protein molecules.

The cosmological term as a source of mass

In the spherically symmetric case, the dominant energy condition, together with the requirement of regularity at the centre, asymptotic flatness and finiteness of the ADM mass, defines the family of asymptotically flat globally regular solutions to the Einstein equations which includes the class of metrics asymptotically de Sitter as r → 0. The source term corresponds to an r-dependent cosmological term Λμν invariant under boosts in the radial direction and evolving from the de Sitter vacuum Λgμν in the origin to the Minkowski vacuum at infinity. The ADM mass is related to a cosmological term by m = (2G)−1∫0∞Λttr2 dr, with the de Sitter vacuum replacing a central singularity at the scale of symmetry restoration. Spacetime symmetry changes smoothly from the de Sitter group near the centre to the Lorentz group at infinity through radial boosts in between. In the range of masses m ≥ mcrit, de Sitter–Schwarzschild geometry describes a vacuum nonsingular black hole (ΛBH), and for m < mcrit, it describes a G-lump—a vacuum self-gravitating particle-like structure without horizons. The quantum energy spectrum of the G-lump is shifted down by the binding energy and zero-point vacuum mode is fixed at the value corresponding (up to the coefficient) to the Hawking temperature from the de Sitter horizon.

Monodromy as topological obstruction to global action-angle variables in systems with coupled angular momenta and rearrangement of bands in quantum spectra

We continue to study the relation between the redistribution of levels in quantum energy spectra and monodromy of the corresponding classical system [see Phys. Lett. A 256, 235 (1999)]. A system with two coupled angular momenta and $\mathrm{SO}(2)$ symmetry is compared to a system with three momenta and $\mathrm{SO}(3)$ symmetry.

Rotational-vibrational relative equilibria and the structure of quantum energy spectrum of the tetrahedral molecule P4

We find relative equilibria (RE) of the rotating and vibrating tetrahedral molecule P4 and study the correspondence of these RE's to the extremal quantum states in the vibration-rotation multiplet and to the extrema of the semi-quantum rotational energy surfaces obtained for a number of excited vibrational states. To compute the energy of RE's we normalize the full rotation-vibration Hamiltonian H of P4 in the approximation of nonresonant modes ν E 2 and ν F_2 3 and find the stationary points of the resulting normal form (known as reduced effective Hamiltonian H eff ) which is defined on the reduced phase space CP 2 × CP 1 × S 2 . Most of these points are fixed points of the symmetry group action on CP 2 × CP 1 × S 2 . To explain our results in more detail we introduce numerical values of the parameters of H, such as the cubic force constants, using an atom-atom harmonic potential with one adjustable parameter. This simple model gives correct qualitative description of the rotational structure of the lowest excited vibrational states ν 2 , ν 3 and ν 2 + ν 3 of P4.

Quantum energy levels and classical periodic orbits: discreteness and statistical duality

It is shown that both universal and non-universal correlations must exist between classical periodic orbits in order that Gutzwiller's semiclassical trace formula is consistent with a real, discrete quantum energy spectrum. Formulae for the two-point correlations are derived. The universal correlations are consistent with those conjectured by Argaman et al. (1993). Likewise, both universal and non-universal correlations must exist between quantum energy levels in order that the trace formula be consistent with the fact that periodic orbit actions are real and discrete. In this case, the two-point correlations implied are consistent with random matrix theory and previous semiclassical calculations. These ideas are illustrated with reference to the primes and the Riemann zeros.

Vibrational Energy-Spectra of Protein Molecules and Non-thermally Biological Effect of Infrared Light

The quantum energy-spectra including high excited states of the protein molecules have been calculated by the discrete nonlinear Schrodinger equation appropriate to protein on the basis of its molecular structure, which are basically consistent with the experimental values obtained by infrared absorption and radiated measurement of person's hands and laser-Raman spectrum from metabolically active E. Coli. From this energy spectra we know that the infrared light with 1–3 μ m and 5–7 μ m wavelength can be absorbed by the protein molecules in the living systems. Thus, in accordance with the non-linear theory of bio-energy transport built and the energy spectra of the protein obtained we give a good account of the biological effect and medical functions of infrared rays absorbed by the living systems which is a non-thermal processes.

Arbitrary trajectory quantization method.

The arbitrary trajectory quantization method (ATQM) is a time dependent approach to quasiclassical quantization based on the approximate dual relationship that exists between the quantum energy spectra and classical periodic orbits. It has recently been shown however, that, for polygonal billiards, the periodicity criterion must be relaxed to include closed almost-periodic (CAP) orbit families in this relationship. In light of this result, we reinvestigate the ATQM and show that at finite energies, a smoothened quasiclassical kernel corresponds to the modified formula that includes CAP families while the delta function kernel corresponding to the periodic orbit formula is recovered as E-->infinity. Several clarifications are also provided.

Quantization ofthe quasiparticle spectrum in the mixed state of d-wavesuperconductors

We have investigated the distinctive features of the band spectrum, eigenfunctions, and density of states (DOS) for low-lying quasiparticle excitations in the mixed state of clean d-wave superconductors (Hc1<<H<<Hc2). Our study is based on an approximate analytical solution of the Bogoliubov-de Gennes equations for quasiparticles with momenta close to gap node directions. Both the quantized energy spectrum and the spatially averaged residual DOS are shown to depend fundamentally on the vortex lattice geometry.

Scars of periodic orbits in the stadium action billiard

Compact billiards in phase space, or action billiards, are constructed by truncating the classical Hamiltonian in the action variables. The corresponding quantum mechanical system has a finite Hamiltonian matrix. In previous papers we defined the compact analog of common billiards, i.e., straight motion in phase space followed by specular reflections at the boundaries. Computation of their quantum energy spectra establishes that their properties are exactly those of common billiards: the short-range statistics follow the known universality classes depending on the regular or chaotic nature of the motion, while the long-range fluctuations are determined by the periodic orbits. In this work we show that the eigenfunctions also follow qualitatively the general characteristics of common billiards. In particular, we show that the low-lying levels can be classified according to their nodal lines as usual and that the high excited states present scars of several short periodic orbits. Moreover, since all the eigenstates of action billiards can be computed with great accuracy, Bogomolny's semiclassical formula for the scars can also be tested successfully.

Nonlinear excitations and their energy spectra in one-dimensional bilinearly coupled spin systems.

In this paper we have analyzed the problem of quantum energy spectra with antiferromagnetic bilinearly coupled spin chains of both integer and half-integer values. The method of analysis involved representing the Hamiltonian in second-quantized form followed by a derivation of quantum field equations of motion. These nonlinear equations were solved semiclassically and the subsequent quantum corrections provided criteria for the existence of gaps in the energy spectra. Our results confirm a conjecture of Haldane [Phys. Lett. 93A, 464 (1983); Phys. Rev. Lett. 50, 1153 (1983); J. Appl. Phys. 57, 3359 (1985)] with specific qualifications regarding the strength and next-nearest-neighbor spin-spin interactions.

Low-energy electron transport in alkali halides

A model of electron transport in alkali halides, below 10 eV, is described. It is based on theoretically calculated microscopic cross sections of electron interactions with lattice phonons. Both acoustic and optical scatterings are taken into account, the former being also treated as a quasielastic process that randomizes the electron motion. Monte Carlo calculations based on the model simulate the UV-induced photoelectron emission from CsI. The calculated quantum efficiency and energy spectra are in good agreement with experimental data, in the photon energy range of 6.3–8.6 eV. The probability for an electron to escape from CsI, NaCl, and KCl is provided as a function of its energy and creation depth. A comparison is made between our approach and other phenomenological models.

Two-spin models with classical chaos and different quantum universality classes.

The local fluctuations in the quantum energy spectrum of a classically completely chaotic autonomous dynamical system are expected to be the same as those in the eigenvalues of Gaussian random Hermitian matrices. That relationship between a dynamical system and the random matrix theory is examined here by introducing a model of an autonomous system of two nonlinearly coupled spins. The proposed model can realize all three universality classes---the orthogonal, the unitary, and the symplectic---of Gaussian random matrices depending upon the nature of the nonlinearity. The proposed system evolves in a finite-dimensional Hilbert space which is in contrast with the existing models of autonomous systems requiring an infinite-dimensional Hilbert space for their description. The model is, therefore, not only free from the unpleasant problem of the truncation of the Hilbert space required for numerical work in the case of an infinite-dimensional Hilbert space but can also be used to examine for a dynamical system those aspects of the random matrix theory that are dependent on the dimension of the matrices. Those aspects are of particular interest in the Brownian motion theory of the transition from a Gaussian orthogonal ensemble to a Gaussian unitary ensemble.

Quantum energy spectrum from the integral Schrodinger equation

The integral form of the Schrodinger equation for bound-state levels, considered by Schwinger(1961), is used for evaluation of the energy spectrum. The method is based upon calculation of the series for powers of eigenvalues of the coupling constant, as given by multiple integrals of products of the potential and free Green functions. Some qualitative properties of the solutions can be easily proved in a general way. The integrals are appropriate, in particular, for calculation by means of the Monte Carlo method. The semiclassical approximation is derived for the one-dimensional case. A number of examples show the effectiveness of the method.

Periodic orbits in arithmetical chaos on hyperbolic surfaces

Length spectra of periodic orbits are investigated for some chaotic dynamical systems whose quantum energy spectra show unexpected statistical properties and for which the notion of arithmetical chaos has been introduced recently. These systems are defined as the unconstrained motions of particles on two-dimensional surfaces of constant negative curvature whose fundamental groups are given by number theoretical statements (arithmetic Fuchsian groups). It is shown that the mean multiplicity of lengths l of periodic orbits grows asymptotically like c.e12//l,I to infinity ., Moreover, the constant c (depending on the arithmetic group) is determined.

Compact billiards in phase space

Compact billiards in phase space, or action billiards, are defined by truncating the classical Hamiltonian in the action variables. The corresponding quantum mechanical system has a finite Hamiltonian matrix. In this paper we define the compact analogue of common billiards, i.e. straight motion in phase space followed by specular reflections at the boundaries. Computation of their quantum energy spectra establishes that their properties are exactly those of regular billiards: the short range statistics follow the known universality classes depending on the regular or chaotic nature of the motion, whereas the long range fluctuations are determined by the periodic orbits.

Quantized conductance through a potential barrier

The conductance through a smooth potential barrier in a narrow quantum wire is shown to be quantized. The study of this simple model demonstrates that there are two essential elements for such conductance quantizations in the ballistic regime: a quantized energy spectrum and a nearly-classical transmission or reflection through the potential barrier. In some sense the quantized conductance steps can be viewed as a spetrometer of the quantum wire.

Periodic librations and their effect on the quantum energy spectrum

Classical Hamiltonian systems with time-reversal symmetry have periodic orbits of two kinds-symmetry pairs (rotations) and self-symmetric orbits (librations). For integrable anharmonic oscillators with two freedoms, almost all of periodic orbits of any period are rotation pairs. However, we show that a KAM-type perturbation alters this balance, such that a finite fraction of the low-period orbits are librations. The generic bifurcations undergone by librations are isomorphic to those of non-symmetric orbits of structurally stable Hamiltonians, with the addition of an extra type of periodic bifurcation. We determine the unfolding of this bifurcation as time-reversal symmetry is broken. The effect of this non-structurally stable bifurcation on the quantum mechanical density of states is also obtained. The present results also hold for systems that are symmetric with respect to general anti-unitary symmetries in quantum mechanics, corresponding to anticanonically reversible Hamiltonian classical systems.

Toward a path integral quantization of Q-balls

Q-balls are time-dependent solitons present in many field theories with unbroken global internal symmetries. To examine the quantized energy spectrum of such objects with Lie groups as internal symmetry groups, we apply group projection techniques to a functional integbral method developed by Dashen, Hasslacher and Neveu. This analysis treats only in the internal symmetry zero modes of such field theories, discussed via their quantum mechanical analogues, since the subtleties of quantization stem largely from the internal symmetry. Examples of U(1) symmetry and SU( n) symmetry on the internal spaces S 1, S 2, and SU( n) are presented.

Super-Selberg trace formula from the chaotic model

A nonrelativistic superparticle moving freely on the super-Riemann surface of genus g≥2 is investigated. The classical motion is characterized by the super-Fuchsian group. The periodic orbits are unstable and the system is classically chaotic. Quantization is performed in the path integral method. The kernel function is explicitly given in the semiclassical approximation. The quantized energy spectrum is related to the length spectrum of the classical periodic orbits, which is a superanalog of Selberg’s trace formula.