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We re-examine the theory of Raman scattering in cubic crystals. The unconventional vector potential of vortex light leads to new selection rules. We show that in this novel optical process, (a) silent phonon modes become active and (b) scattering tensors change for ordinary Raman active phonon modes. Calculation based on a simplified model shows that the vortex Raman scattering intensity can be comparable with that of ordinary Raman process.

We performed group theoretical investigation on symmetries of excitations in 3D topological insulators (TI) Bi2Te3, Bi2Se3 and Sb2Te3. Selection rules of transitions from bulk states (BS) to bulk states, surface states (SS) to surface states and bulk states to surface states are studied over the entire Brillouin zone. A new representation group G′ is constructed to deal with transitions between surface states and bulk states. Both direct and indirect optical transitions are studied. We also derive selection rules for scattering between SS and phonons. Our group theory analysis shows that SS is protected from scattering by both spatial symmetry and topology: many SS scattering channels are forbidden by symmetry and topological protection further suppresses the symmetry allowed scattering. Our analysis can provide an explanation of some ARPES results and Raman experiments.

The Ginzburg-Landau theory is analyzed in the case of small dimension superconductors, a couple of orders of magnitude above the coherence length, where the theory is still valid but quantum fluctuations become significant. In this regime, the potential around the expectation value is approximated to a quadratic behavior, and the ground-state derived from the Klein-Gordon solutions of the Higgs-like field. The ground-state energy is directly compared to the condensation energy, and used to extract new limits on the size of superconductors at zero Kelvin and near the critical temperature., 4 pages, 1 figure

We propose using coherent optical spectroscopy to study and control optically-forbidden (dark) biexciton states in crystals of cuprous oxide. These states are revealed in the correlation spectra cross resonances due to coherence with the quadrupole allowed 1S exciton manifold. The signal is obtained by means of sum-over-state formalism and comparing equations of motion for the weakly interacting quadrupole excitons with their analogue of non-interacting quasiparticles. The dephasing mechanisms include rapid Auger relaxation of biexcitons which allegedly impedes the Bose–Einstein condensation of quadrupole excitons. An interesting effect attributed to the deviation of the quadrupole excitons from the ortho–para excitons picture is that the positions of the biexciton resonances are defined by the energy splitting between and excitons and can be tuned by an external perturbation. Possible quantum computing and lasing applications of the quadrupole induced chirality effects of the excitons and biexcitons, and coherence between exciton/biexciton manifolds are discussed.

Hermann proposed that mesomorphic media should be classified by assigning certain "statistical symmetry groups" to each possible partially ordered array. Two translational groups introduced were called superordinate and subordinate. We find that the average density in such a partially ordered medium has the superordinate symmetry ℒ1, while the pair correlation function has the subordinate symmetry ℒ2. A complete listing is made of all compatible combinations of ℒ1 and ℒ2 in two and three dimensions. This leads to more possible symmetries than Hermann obtained, e.g., also to nonstoichiometric crystals. The order parameter space for the systems is found to be the quotient space ℒ1/ℒ2. In most cases it is identical to the order parameter space of low-dimensional XY spin systems. The Landau free energy is expanded as functional of the two-particle correlation function K; the translation group is found to be ℒ1×ℒ2. A Landau mean-field theory can then be carried out by expanding the system free energy into a series of invariants of the active irreducible representations of K and mapping the free energy onto that for an XY planar spin system. We predict novel critical behavior for transitions between mesomorphic phases and “go nogo” selection rules for continuous transitions. We give the structure factors for X-ray scattering so changes in all such phase transitions are observable. The statistical symmetry groups, which describe point and translational symmetries of the mesophases, are classified. Proposals are made to include quasi-long-range or topological order in the classification scheme.

The authors would like to thank the Center for Theoretical Physics of the Physics Department at the New York City College of Technology, for providing computing power from their High-Performance Computing Cluster. The work of M.C.N. Fiolhais was supported by FCT Grant No. SFRH/BPD/100379/2014. The work of C. M. Pease was partly supported by Macaulay Honors College. The authors would also like to thank Juan Antonio Aguilar-Saavedra and Nuno F. Castro for a long time collaboration., The latest and most precise top quark measurements at the LHC and Tevatron are used to establish new limits on the Wtb vertex. Recent results on the measurements of the W-boson helicity fractions and single top quark production cross section are combined in order to establish new limits at 95% CL (confidence level). The allowed regions for these limits are presented, for the first time, in three-dimensional graphics, for both real and imaginary components of the different anomalous couplings, providing a new perspective on the impact of the combination of different physics observables. These results are also combined with the prospected future measurement of the single top quark production cross section and W-boson helicity fractions at the LHC., The authors would like to thank the Center for Theoretical Physics of the Physics Department at the New York City College of Technology, for providing computing power from their High-Performance Computing Cluster. The work of M.C.N. Fiolhais was supported by FCT Grant No. SFRH/BPD/100379/2014. TheworkofC.M.PeasewaspartlysupportedbyMacaulay Honors College. The authors would also like to thank Juan Antonio Aguilar-Saavedra and Nuno F. Castro for a long time collaboration.

The formation of a hybridization state of Wannier Mott exciton and Frenkel exciton in different hetero-structure configurations involving quantum dots is investigated. The hybrid excitons exist at the interfaces of the semiconductors quantum dots and the organic medium, having unique properties and a large optical non-linearity. The coupling at resonance is very strong and tunable by changing the parameters of the systems (dot radius, dot–dot distance, generation of the organic dendrites and the materials of the system etc…). Different semiconductor quantum dot–organic material combination systems have been considered such as a semiconductor quantum dot lattice embedded in an organic host, a semiconductor quantum dot at the center of an organic dendrite, a semiconductor quantum dot coated by an organic shell.

A U(3) model proposed by Iachello for superconductivity in cuprate materials is analyzed. The model consists of s and d pairs (approximated as bosons) in a two-dimensional Fermi system with a surface. The transition occurs between a phase in which the system is a condensate of one of the bosons, and a phase which is a mixture of two types of bosons. In the current work we have investigated the validity of the Bogoliubov approximation, and we used a reduced Hamiltonian to determine a phase diagram, the symmetry of the phases and the temperature dependence of the heat capacity.

In this paper we present an analytical method for solving the Gross-Pitaevskii equation for the Bose-Einstein condensation in the dilute atomic alkali gases. Using a variational ansatz, we are able to obtain an analytical solution for the order parameter and for the chemical potential as a function of a unique universal parameter: λ/(ħ ω l) (l is the oscillator length, ω the trap frequency and λ an effective coupling constant). We also perform a comparative analysis between our method of solution and two other methods with defined range of validity: the perturbation theory and the Thomas-Fermi Approximation (TFA). The presented method is valid for negative and for positive self interactions as well. In the positive coupling constant region it is consistent with the TFA, extending its validity beyond the limits of validity of this well known approximation, towards small and negative values of the self-interaction coupling constant. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The quantum phase transitional behavior of the U ( 3 ) boson model is studied. Low-lying levels, overlaps of wavefunctions with those in the d-wave dominant and s- and d-wave mixed phases, as well as ground state occupation probabilities of s- and d-components are examined as functions of the control parameter and the number of particles. The results indicated that the s- and d-wave component change in the wavefunction possibly is a first order quantum phase transition in the large N limit.

We show that an array of semiconductor quantum dots in an organic host leads to a large two-photon absorption. The optical nonlinearity depends on the semiconductor, the dot size, and the dot-to-dot spacing. Using numerical simulations, we demonstrate that a large optical limiting is possible using thin films of this hybrid material.

A quasiclassical theory for DC magnetotransport in a modulated quantum Hall system near filling factor ν=½ is presented. A weak one-dimensional electrostatic potential acts on the two-dimensional electron gas. Closed form analytic expressions are obtained for the resistivity ρ⊥ corresponding to a current at right angles to the direction of the modulation lines as well as a smaller component ρ‖ for a current along the direction of the modulation lines. It is shown that both resistivity components are affected by the presence of the modulation. Numerical results are presented for ρ⊥ and ρ‖ and show reasonable agreement with the results of recent experiments.

We use the method of group contractions to relate wavelet analysis and Gabor analysis. Wavelet analysis is associated with unitary irreducible representations of the affine group while the Gabor analysis is associated with unitary irreducible representations of the Heisenberg group. We obtain unitary irreducible representations of the Heisenberg group as contractions of representations of the extended affine group. Furthermore, we use these contractions to relate the two analyses, namely, we contract coherent states, resolutions of the identity, and tight frames. In order to obtain the standard Gabor frame, we construct a family of time localized wavelet frames that contract to that Gabor frame. Starting from a standard wavelet frame, we construct a family of frequency localized wavelet frames that contract to a nonstandard Gabor frame. In particular, we deform Gabor frames to wavelet frames.

We investigate a new hybrid exciton state which arises when a regular array of semiconductor quantum dots is placed in a molecular organic medium. The multipolar interaction of excitons in different dots form a type of Wannier–Mott exciton transfering among the dot array. Then a new eigenstate arises owing to strong dipole–dipole coupling of these Wannier excitons of the dots and the Frenkel excitons of the organic molecules. The new state has a large oscillator strength (Frenkel-like) and a large exciton Bohr radius (Wannier-like). Strong enhancement of linear and nonlinear optical responses occurs. Numerical estimates are made for ZnSe dots in a typical organic host.

We consider the effect of local flattening on the Fermi surface (FS) of a metal upon geometric oscillations of the velocity and attenuation of ultrasonic waves in the neighborhood of the acoustic cyclotron resonance. It is shown that such peculiarities of the local geometry of the FS can lead to a significant enhancement of both cyclotron resonance and geometric oscillations. Characteristic features of the coupling of ultrasound to shortwave cyclotron waves arising due to the local flattening of the FS are analyzed. PACS numbers 71.18.+y; 72.15.Gd; 72.15.-v, 8 pages, 3 figures, text revised

The dynamical analog of the Kohn Anomaly image of the Fermi Surface is demonstrated for the response functions to the surface acoustic waves in Quantum Hall Systems near $\nu = 1/2$. Kinks appear in the velocity shift $Delta s/s$ and attenuation coefficient $\Gamma$. The effect is considerably enhanced under periodic modulation and should be observable., Comment: 5 pages, 2 figures, the published version

We introduce a new generic model of a deformed Composite Fermion-Fermi Surface (CF-FS) for the Fractional Quantum Hall Effect near $/nu=1/2$ in the presence of a periodic density modulation. Our model permits us to explain recent Surface Acoustic Wave observations of anisotropic anomalies [1,2] in sound velocity and attenuation- appearance of peaks and anisotropy - which originate from contributions to the conductivity tensor due to regions of the CF-FS which are flattened by the applied modulation. The calculated magnetic field and wave vector dependence of the CF conductivity,velocity shift and attenuation agree with experiments., Revised manuscript (cond-mat/9807044) 23 September 1998; 10 pages

A perturbation Brillouin-Wigner approach to anisotropic exciton problem, based on a hyperspherical formalism, is developed. The binding energies and oscillator strengths of elongated as well as flattened excitons are calculated numerically. It is shown that with an increase of the anisotropy degree the oscillator strengths are markedly redistributing between optically active and formerly inactive states, making the latter optically active.

We analyze single-electron or exciton transport in long molecules in the presence of both static disorder and temporal noise both of which inevitably exist in biological systems. The equations for the density matrix are derived within an approximation that the temporal noise of transition amplitudes is not correlated. Our model predicts that while in the short-time limit the transport remains coherent, for sufficiently long time the temporal noise causes destruction of the phase coherence, and a crossover from coherent to diffusive transport takes place. This effect leads to the power-law asymptotic behavior of the transmission coefficient with the exponent depending on the effective dimensionality of the molecule.

A simple theoretical model for the origin of spontaneous polarization in nanocrystals is developed. We propose that the origin of the spontaneous polarization is in the boundary layer between “cap” and the nanocrystal, and the internal electric field in the dot is due to the piezoelectric effect caused by the strain existing in the interface region of materials with different lattice constants. The model, based on spherical rotation symmetry without inversion [SO(3)], employs a distribution of polarization with symmetry which is a subgroup of SO(3) consistent with the hexagonal structure of wurtzite structure. We predict the internal electric field and compare with experimental data.

The gauge symmetry of the Ginzburg-Landau theory for two-gap superconductors is analyzed in this letter. We argue that the existence of two different phases, associated with the two independent scalar Higgs fields, explicitly breaks the gauge symmetry of the Ginzburg-Landau hamiltonian, unless a new additional vector field is included. Furthermore, the interference term, or Josephson coupling, holding a direct dependence with the phase difference, also explicitly breaks down the gauge symmetry. We show that a solution for the problem is achieved by adding an additional kinetic coupling term between the two vector fields, which generates the desired terms through a spontaneous symmetry breaking mechanism. Finally, the electrodynamics of the system is also presented in terms of the supercurrents inside the superconducting region., Comment: 3 pages

Quantum evolution of a collective mode of a Bose-Einstein condensate containing a finite number N of particles shows the phenomena of collapses and revivals. The characteristic collapse time depends on the scattering length, the initial amplitude of the mode and N. The corresponding time values have been derived analytically under certain approximation and numerically for the parabolic atomic trap. The revival of the mode at time of several seconds, as a direct evidence of the effect, can occur, if the normal component is significantly suppressed. We also discuss alternative means to verify the proposed mechanism.

We derive a new expression for the current of one-dimensional anyons in terms of Jack polynomials and calculate the exact dynamical polarization tensor for all rational values of the statistical parameter λ. We employ the method of expansion of operators in terms of many-body eigenfunctions.

The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a sufficiently large number of particles, crossover transitions become sharp, so that symmetry breaking happens similarly to that in macroscopic systems. This concerns, in particular, global gauge symmetry breaking, related to Bose–Einstein condensation and superconductivity, or isotropy breaking, related to the generation of quantum vortices, and the stratification in multicomponent mixtures. A special type of symmetry transformation, characteristic only for finite systems, is the change of shape symmetry. These phenomena are illustrated by the examples of several typical mesoscopic systems, such as trapped atoms, quantum dots, atomic nuclei, and metallic grains. The specific features of the review are: (i) the emphasis on the peculiarities of the symmetry breaking in finite mesoscopic systems; (ii) the analysis of common properties of physically different finite quantum systems; (iii) the manifestations of symmetry breaking in the spectra of collective excitations in finite quantum systems. The analysis of these features allows for the better understanding of the intimate relation between the type of symmetry and other physical properties of quantum systems. This also makes it possible to predict new effects by employing the analogies between finite quantum systems of different physical nature.

Evanescent field Raman scattering (EFRS) of light by phonons in perfect crystals is proposed as a method to investigate spectra of vibrations from the entire Brillouin zone. A boundary between the crystal, and the waveguide providing the evanescent field into the crystal depth ensures violation of the momentum conservation perpendicular to the boundary. As a consequence, Raman scattering by phonons from the entire Brillouin zone can be observed. A parabolic region of the phonon dispersion curve demonstrates a specific asymmetric EFRS line as a function of the energy transfer. Location of the parabolic regions in the momentum space, and the mode dispersion can be identified.

A new approach to the theory of anisotropic exciton based on Fock transformation, i.e., on a stereographic projection of the momentum to the unit 4-dimensional (4D) sphere, is developed. Hyperspherical functions are used as a basis of the perturbation theory. The binding energies, wave functions and oscillator strengths of elongated as well as flattened excitons are obtained numerically. It is shown that with an increase of the anisotropy degree the oscillator strengths are markedly redistributed between optically active and formerly inactive states, making the latter optically active. An approximate analytical solution of the anisotropic exciton problem taking into account the angular momentum conserving terms is obtained. This solution gives the binding energies of moderately anisotropic exciton with a good accuracy and provides a useful qualitative description of the energy level evolution., 23 pages, 8 figures

A new symmetry is identified for the many particle q-Bose system, which permits carrying out a linear q-canonical transformation, i.e., one which preserves the q-deformed commutation rules. The symmetry is exhibited when the set of q-modes is partitioned into "positive" and "negative," each subset having its own type of deformation. For plane-wave modes, labelled by wave vector k, this means separate positive and negative wave vectors. Then, identifying the new symmetry: (q → q−1, k → −k) the transformation can be implemented. The new aspect is the simultaneous transformation of wave vector k and parameter q.

The identification of alloy systems of AlMn and other compounds with macroscopic icosahedral symmetry has been reported. In this work we discuss several macroscopic tensor properties which may distinguish between icosahedral point group symmetry I, from either full isotropic SO (3) symmetry, or cubic 0 symmetry. Emphasis is given to the structure of the third order elastic coefficient tensor and the non-linear elastic coefficients which arise in I-symmetry systems. Corresponding sound velocities are obtained: these can permit experimental measurements using ultrasonic techniques

The “generalized coherent state” representation was applied to the model hamiltonian, describing the light propagation in a tenuous inhomogeneous dielectric medium. For multimode squeezed states, the “equation of motion” for squeezing and other parameters were derived. Some approximate solutions obtained suggest that under certain conditions the squeezing parameter may be increased due to the interaction between different modes in a process of multiple scattering.

Phonons in a lossless phonon-polariton exhibit remarkable non-classical features. In the small wavevectors side of the polariton energy spectrum, the phonon population in a phonon-polariton coherent state exhibits strong oscillations. This is caused by the highly non-classical structure of the phonon-polariton state in that region of the spectrum. A neutron scattering experiment enables one to probe the non-classical nature of a phonon-polariton state.

We report calculated substantial enhancement of the second harmonic generation (SHG) in cuprous oxide crystals resonantly hybridized with an appropriate organic material (DCM2:CA:PS 'solid-state solvent'). The quadrupole origin of the inorganic part of the quadrupole-dipole hybrid provides inversion symmetry breaking and the organic part contributes to the oscillator strength of the hybrid. We show that the enhancement of the SHG, compared to bulk cuprous oxide crystal, is proportional to the ratio of the DCM2 dipole moment and the effective dipole moment of the quadrupole transitions in the cuprous oxide. It is also inversely proportional to the line-width of the hybrid and bulk excitons. The enhancement may be regulated by adjusting the organic blend (mutual concentration of the DCM2 and CA part of the solvent) and pumping conditions(varying the angle of incidence in case of optical pumping or populating the minimum of the lower branch of the hybrid in case of electrical pumping)., 8 pages, 3 figures

For any Inonu-Wigner contraction of a three dimensional Lie algebra we construct the corresponding contractions of representations. Our method is quite canonical in the sense that in all cases we deal with realizations of the representations on some spaces of functions; we contract the differential operators on those spaces along with the representation spaces themselves by taking certain pointwise limit of functions. We call such contractions strong contractions. We show that this pointwise limit gives rise to a direct limit space. Many of these contractions are new and in other examples we give a different proof.

In this paper, we present a unique procedure, with physical justification, for the hierarchical construction of quantum Hall states (QHS). We have connected the hierarchy structure of the filling fractions of QHS constructed using our rule with the Farey-number hierarchy structure. This connection reveals that our hierarchy structure is self-similar. Based on this hierarchy structure, we propose a renormalization-group (RG) flow diagram for the scaling behavior of transitions between Hall plateaus. We discuss and compare our results with Jain's hierarchy theory and other previous scaling theories of the quantum Hall effect. The difference can be examined by future experiments.

We have derived an exact Breit-Wigner formula for the conductivity of a strongly disordered system using the Schwinger-Keldysh Green's-function method. Using this theory we study a generalized one-dimensional Anderson model (with random site energies and random hopping matrix elements) in the present paper. Numerical calculations show that our model describes the coherent feature of resonant tunneling in strongly disordered mesoscopic systems. If one single-site energy is changed, the magnitude of steady current changes drastically; in fact, resonant tunneling can be destroyed

An isomorphism is realized between the (q)-deformed harmonic oscillator and a particular anharmonic oscillator model: it permits insight into the problem of the physics behind the deformation parameter q. In our model, the anharmonic coupling strength is shown to be proportional to q. The isomorphism permits us also to analyze and to interpret the appearance of various nonclassical features induced by a q deformation during the time evoluton of an su(2) coherent state

Collective excitations such as excitons and spin waves, in many-body condensed matter systems have long been described as “almost bosons”. I make the Ansatz that collective excitations are exactly described by quantum-deformed canonical commutation rules (QDCCR): previous results are then lowest approximations to these rules. The q-deformed spectrum produces altered conditions for “q-Bose condensation”.

We studied intrinsic bistability in a double-barrier resonant-tunneling structure using the noneguilibrium Schwinger-Keldysh formalism. We derive and solve a nonlinear integral equation for the charge density in the quantum well and the current as a function of bias voltage and charge density. We calculated the I-V curves for a typical GaAs/(Al,Ga)As double-barrier structure at different temperature. The effect of temperature and resonant-energy-level broadening (including scattering effect) on the intrinsic bistability is discussed

Certain thermal (Matsubara) Green functions are obtained for a “free” system of quantum-deformed harmonic oscillators. It is shown that the form of the single-particle Matsubara function is changed, with an explicit dependence on s = 1n q appearing in a simple form and suggesting that quantum-deformed commutation rules intrinsically incorporate interactions even in the “free case”. A two-particle Matsubara function gives no evidence of a bound state energy shift.

A simple model is proposed for the photoluminescent emission spectrum in the fractional quantum Hall system. In this model we show that the expression for the emission intensity I(ω) can be factorized into an excitonlike part and a portion which depends explicitly on the dynamical structure factor S(q,ω) for the unperturbed quantum Hall state. For the observed E 0 line the model explains a series of intensity minima which occur at the onset of each plateau in σ xy for ν=2/3, 7/11, 3/5, and 4/7, superimposed on a general rising trend versus applied magnetic field B

Etude de la dispersion excitonique dans les puits quantiques multiples (MQW) et dans les superreseaux, a l'aide du modele de liaison forte. L'interaction coulombienne entre les etats excitoniques dans des puits differents induit une interaction dipole-dipole effective, meme lorsque l'effet tunnel est neglige. Un aspect distinctif de la relation de dispersion excitonique est que, lorsque le vecteur d'onde approche la valeur zero a partir de directions differentes (perpendiculaire ou parallele a la direction de la croissance), l'energie limitante prend des valeurs differentes. Ceci constitue une contribution intrinseque remarquable a la largeur de la raie de l'exciton, qui est de l'ordre du meV pour les puits GaAs-Al x Ga 1−x As

We have developed an algorithm for the computation of the Molien function (generating for the multiplicity of the identity representation in the symmetrized nth power of representation P of group G) and used it to compute the Molien function for irreducible representations of crystal space groups. The calculation is illustrated upon some irreducible representations of the crystal space groups. Ir. particular, a case of interest is some irreducible representations of the crystal space group 0 h 3 -Pn3m. Quartic invariants are exhibited for irreducible representations *X (j) and *R (j)j= 1,2,3,4 of 0 O h 3 .

Results of a RG theory of phase transitions in A-15, or Pm3n structure are discussed and compared to the Landau theory results.

A review is given of group-theory related aspects of the Landau-Thermodynamic Theory of continuous phase transitions in crystals. The review discusses developments of the theory during several time intervals. First interval: the 25 years (1937–62) after the theory was presented; Second interval (1962-77) covers the recent 15 years; Third interval (1977- ) presents some possible directions for work in the future. Thus the first 40 years of this theory were characterized inter alia by elaborations and applications of the group theory aspects of the problem which Landau examined: Given a system with group G; What groups G → G′,... may be achieved by continuous transitions i.e. G → G′,...? What order parameters are consistent with transitions G → G′, or G → G′, ...?

Some aspects of post-conventional polariton physics are discussed. In the framework of quantum statistical properties we demonstrate that polaritons are intrinsically squeezed. The polariton squeezing is frequency tunable, and can be larger than that in usual atomic systems. The new phonoriton excitation, which gives rise to spectrum reconstruction, is reexamined on the basis of a simple model: threshold behavior, new gap structure and related properties are discussed.

The “phonoriton” is an elementary excitation constructed from an exciton-polariton and phonon in semiconductors under intense excitation near the exciton resonance. In this paper we describe its basic properties using a simple model. We propose two experiments: Non-Linear Resonant Brillouin Scattering and Non-Linear modulation reflectivity to determine the new phonoriton spectrum. Quantitative analysis shows that the phonoriton effects are expected to be measurable.