arXiv subjects

Joseph L. Birman

Publications and source records attributed to Joseph L. Birman.

At least 19 recordsLinked to original sources

arXiv2017

Gabor analysis as contraction of wavelets analysis

We use the method of group contractions to relate wavelets analysis and Gabor analysis. Wavelets analysis is associated with unitary irreducible representations of the affine group while 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 wavelets frames that contract to that Gabor frame. Starting from a standard wavelets frame we construct a family of frequency localized wavelets frames that contract to a nonstandard Gabor frame. In particular we deform Gabor frames to wavelets frames.

math.RT↗

arXiv2015

Size Effects in the Ginzburg-Landau Theory

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.

cond-mat.supr-con↗

arXiv2014

Gauge Invariance and Spontaneous Symmetry Breaking in Two-Gap Superconductors

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.

cond-mat.supr-con↗

arXiv2014

Phenomenological correlations in high-temperature superconductors

An interpretation of the quadratic parameter of the Ginzburg-Landau theory of superconductivity is presented in this paper. The negative term in the potential, which allows the spontaneous symmetry breaking, is interpreted as a direct contribution from the energy gap at the Fermi surface to the effective potential. As a result, in the London approximation of the Ginzburg-Landau theory for type-II superconductors, a strong correlation is predicted and observed between the upper critical field at zero kelvin and the critical temperature in high temperature superconductors.

cond-mat.supr-con↗

arXiv2014

One dimensional zone center phonons in $O_{h}$ space group

Motivated by experiments, we performed a systematic study on the one dimensional zone center phonons in $O_{h}$ space groups. All the one dimensional phonon modes for different Wyckoff positions are tabulated. We show that at least four (inequivalent) atoms (in one set of Wyckoff positions) are needed to carry a single one dimensional phonon. A general restriction rule on the number of atoms and the number of one dimensional phonons is obtained. The same restriction applies to phonons of all cubic crystal systems ($T$, $T_{h}$, $T_{d}$, $O$, $O_{h}$) and to magnons for crystals whose unitary symmetry elements are in ($T$, $T_{h}$, $T_{d}$, $O$, $O_{h}$). Crystals with $A15$ structure are found to satisfy experimental requirements (to have a $Γ_{2}^{+}$ phonon) while most crystals of $O_{h}$ space groups do not. $A15$ is also used to demonstrate the rules we found regarding the phonon structure in $O_{h}$ space groups.

cond-mat.mtrl-sci↗

arXiv2014

Decomposition of direct product at an arbitrary Brillouin zone point: $D^{(\bigstar{R})(m)}$ $\otimes$ $D^{(\bigstar{-R})(m)}$

A general rule is presented for the decomposition of the direct product of irreducible representation at arbitrary Brillouin zone point $\bf{R}$ with its negative: the number of the appearences of the zone center representation equals the dimensionality of the representation. This rule is applicable for all space groups. Although in most situations the interesting physics takes place at high symmetry points in the Brillouin zone, this general rule is useful for situations where double excitations are considered. It is shown that double excitations from arbitrary Brillouin point $\bf{R}$ have the right symmetry to participate in all optical experiments regardless of polarization directions.

cond-mat.mtrl-sci↗

arXiv2012

On the contraction of so(4) to iso(3)

For any skew-Hermitian integrable irreducible infinite dimensional representation $η$ of $iso(3)$, we find a sequence of (finite dimensional) irreducible representations $ρ_n$ of $so(4)$ which contract to $η$.

math-ph↗

arXiv2012

Hyperspherical theory of anisotropic exciton

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.

math-ph↗

arXiv2012

Optical selection rules in topological insulators Bi$_2$Sb$_3$, Bi$_2$Se$_3$, Bi$_2$Te$_3$ and Sb$_2$Te$_3$

We performed group theoretical investigation of symmetries of excitations in topological insulators \ce{Bi2Sb3}, \ce{Bi2Te3}, \ce{Bi2Se3} and \ce{Sb2Te3}, focusing on selection rules for optical processes. Electronic transitions of bulk states to bulk states, surface states to surface states and bulk states to surface states are studied over the entire Brillouin zone. A new technique is used to deal with transitions between surface states and bulk states. Time reversal symmtry is also included in the analysis. Our results show that only (Γ), (Λ) and (M) points of the Brillouin zone would depend on light polarization for transitions between bulk states and surface states. As an example of application, electron spin polarizations of photoelectrons are calculated at (Γ) point. A general rule for the direct product between the representation at an arbitrary point in the Brillouin zone with itself is presented.

cond-mat.mes-hall↗

arXiv2008

Theory of enhanced second-harmonic generation by the quadrupole-dipole hybrid exciton

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).

cond-mat.mtrl-sci↗

arXiv2007

Formal analytical solutions for the Gross-Pitaevskii equation

Considering the Gross-Pitaevskii integral equation we are able to formally obtain an analytical solution for the order parameter $Φ(x)$ and for the chemical potential $μ$ as a function of a unique dimensionless non-linear parameter $Λ$. We report solutions for different range of values for the repulsive and the attractive non-linear interactions in the condensate. Also, we study a bright soliton-like variational solution for the order parameter for positive and negative values of $Λ$. Introducing an accumulated error function we have performed a quantitative analysis with other well-established methods as: the perturbation theory, the Thomas-Fermi approximation, and the numerical solution. This study gives a very useful result establishing the universal range of the $Λ$-values where each solution can be easily implemented. In particular we showed that for $Λ<-9$, the bright soliton function reproduces the exact solution of GPE wave function.

cond-mat.other↗

arXiv2007

Theory of enhanced dynamical photo-thermal bi-stability effects in cuprous oxide/organic hybrid heterostructure

We theoretically demonstrate the formation of multiple bi-stability regions in the temperature pattern on the interface between a cuprous oxide quantum well and DCM2:CA:PS organic compound. The Frenkel molecular exciton of the DCM2 is brought into resonance with the $1S$ quadrupole Wannier-Mott exciton in the cuprous oxide by "solvatochromism" with CA. The resulting hybrid is thermalized with surrounding helium bath. This leads to strongly non-linear temperature dependence of the laser field detuning from the quadrupole exciton energy band which is associated with the temperature induced red shift of the Wannier exciton energy. Numerical up and down-scan for the detuning reveals hysteresis-like temperature distribution. The obtained \emph{multiple} bi-stability regions are at least three orders of magnitude bigger ($meV$) than the experimentally observed bi-stability in bulk cuprous oxide ($μeV$). The effective absorption curve exhibits highly asymmetrical behavior for the Frenkel-like (above the $1S$ energy) and Wannier-like (below the $1S$ energy) branches of the hybrid.

cond-mat.mtrl-sci↗

arXiv2007

Evanescent quadrupole polariton

In the work we demonstrate the formation of new type of polariton on the interface between a cuprous oxide slab and a polystyrene micro-sphere placed on the slab. The evanescent field of the resonant whispering gallery mode (WGM) has a substantial gradient, and therefore effectively couples with the quadrupole $1S$ excitons in cuprous oxide. This evanescent polariton has a long life-time ($1.7 ns$), which is determined only by its excitonic component. The polariton lower branch has a well pronounced minimum. This suggests that this excitation can be utilized for BEC. The spatial coherence of the polariton can be improved by assembling the micro-spheres in a linear chain.

cond-mat.mtrl-sci↗

arXiv2007

Polaritons in cuprous oxide perturbed by LA-phonons

We present a comparative analysis of a 'conventional' phonoriton (coherent superposition of exciton-photon-phonon) and a polariton (coherent exciton-photon superposition) 'weakly' coupled to the LA-phonons bath. Depending on duration of the pumping laser field the phonon-induced decoherence results in two distinct types of excitation. Long ($ms$) laser pumping pulses form an 'equilibrium' polariton. The generic feature here is a pronounced photo-thermal bi-stability. i.e. formation of four distinct branches. Transitions between branches can be achieved by excitation energy fluctuations as small as $200 neV$ which may impede BEC of the para-excitons. Short ($μs$) laser pulses create a 'quasi-equilibrium' polariton. In the latter case, for some critical intensity of the laser field we demonstrate possibility of strong luminicence from a highly unstable localized state on the lower polariton branch.

cond-mat.mtrl-sci↗

arXiv2007

Hybridized quadrupole-dipole exciton effects in $Cu_2O$ - Organic Heterostructure

In the present work we discuss resonant hybridization of the $1S$ quadrupole Wannier-Mott exciton (WE) in a $Cu_2O$ quantum well with the Frenkel (FE) dipole exciton in an adjacent layer of organic DCM2:CA:PA. The coupling between excitons is due to interaction between the gradient of electric field induced by DCM2 Frenkel exciton and the quadrupole moment of the $1S$ transition in the cuprous oxide. The specific choice of the organic allows us to use the mechanism of 'solid state solvation' to dynamically tune the WE and FE into resonance during time $\approx 3.3 \: ns$ (comparable with the big life time of the WE) of the 'slow' phase of the solvation. The quadrupole-dipole hybrid utilizes the big oscillator strength of the FE along with the big lifetime of the quadrupole exciton, unlike dipole-dipole hybrid exciton which utilizes big oscillator strength of the FE and big radius of the dipole allowed WE. Due to strong spatial dispersion and big mass of the quadrupole WE the hybridization is not masked by the kinetic energy or the radiative broadening. The lower branch of the hybrid dispersion exhibits a pronounced minimum and may be used in applications. Also we investigate and report noticeable change in the coupling due to a induced 'Stark effect' from the strong local electric field of the FE. We investigated the fine energy structure of the quantum well confined ortho and para excitons in cuprous oxide.

cond-mat.mtrl-sci↗

arXiv2006

On a theoretical model for d-wave to mixed s- and d-wave transition in cuprate superconductors

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.

cond-mat.supr-con↗

arXiv2006

Su(3) Algebraic Structure of the Cuprate Superconductors Model based on the Analogy with Atomic Nuclei

A cuprate superconductor model based on the analogy with atomic nuclei was shown by Iachello to have an $su(3)$ structure. The mean-field approximation Hamiltonian can be written as a linear function of the generators of $su(3)$ algebra. Using algebraic method, we derive the eigenvalues of the reduced Hamiltonian beyond the subalgebras $u(1)\bigotimes u(2)$ and $so(3)$ of $su(3)$ algebra. In particular, by considering the coherence between s- and d-wave pairs as perturbation, the effects of coherent term upon the energy spectrum are investigated.

cond-mat.other↗

arXiv2006

Theory of coexistence of superconductivity and ferroelectricity

A new investigation of the coexistence and competition of ferroelectricity and superconductivity is reported. In particular we show that the starting Hamiltonian of a previous study by Birman and Weger (2001) can be exactly diagonalized. The result differs significantly from mean-field theory. A Hamiltonian with a different realization of the coupling between ferroelectricity and superconductivity is proposed. We report the results for mean-field theory applied to this Hamiltonian. We find that the order parameters are strongly affected by this coupling.

cond-mat.supr-con↗