Realization Of SU Research Articles

Universal Kardar-Parisi-Zhang Dynamics in Integrable Quantum Systems.

Although the Bethe ansatz solution of the spin-1/2 Heisenberg model dates back nearly a century, the anomalous nature of its high-temperature transport dynamics has only recently been uncovered. Indeed, numerical and experimental observations have demonstrated that spin transport in this paradigmatic model falls into the Kardar-Parisi-Zhang (KPZ) universality class. This has inspired the significantly stronger conjecture that KPZ dynamics, in fact, occur in all integrable spin chains with non-Abelian symmetry. Here, we provide extensive numerical evidence affirming this conjecture. Moreover, we observe that KPZ transport is even more generic, arising in both supersymmetric and periodically driven models. Motivated by recent advances in the realization of SU(N)-symmetric spin models in alkaline-earth-based optical lattice experiments, we propose and analyze a protocol to directly investigate the KPZ scaling function in such systems.

Hyperfine Splitting of Excited States of New Heavy Hadrons and Low-Energy Interaction of Hadronic Dark Matter with Photons, Nucleons, and Leptons

We consider the structure of excited states and low-energy interaction of hadronic dark matter with photons, leptons, and nucleons. Description of the lowest excited levels is fulfilled in an analogy with the standard heavy-light mesons. Using the effective vertex of new heavy hadrons interaction with W-boson, we calculate cross-section of the lepton scattering on the dark matter particle. Analysis of strong low-energy interaction of new hadrons was carried out within the effective meson-exchange model based on dynamical realization of SU(3)-symmetry. A cross-section of nucleon scattering on the hadronic dark matter was also calculated using this model. The most essential phenomenological consequences of the low-energy dark matter interaction with leptons and nucleons are discussed.

Interaction of Hadronic Dark Matter with Nucleons and Leptons

We analyze the low-energy Lagrangian of hadronic dark matter interaction with nucleons and leptons. The analysis was fulfilled within the framework of the effective meson-exchange model, which is based on dynamic realization of SU(3)-symmetry. Using this Lagrangian, we calculate the cross-section of low-energy scattering of nucleons on hadronic dark matter particles. Effective vertex of W-boson interaction with new hadrons is constructed and the cross-section of lepton scattering on dark matter particles is calculated.

Spinning extensions of D(2, 1; \u03b1) superconformal mechanics

As is known, any realization of SU(2) in the phase space of a dynamical system can be generalized to accommodate the exceptional supergroup D(2, 1; α), which is the most general mathcal{N} = 4 supersymmetric extension of the conformal group in one spatial dimension. We construct novel spinning extensions of D(2, 1; α) superconformal mechanics by adjusting the SU(2) generators associated with the relativistic spinning particle coupled to a spherically symmetric Einstein-Maxwell background. The angular sector of the full superconformal system corresponds to the orbital motion of a particle coupled to a symmetric Euler top, which represents the spin degrees of freedom. This particle moves either on the two-sphere, optionally in the external field of a Dirac monopole, or in the SU(2) group manifold. Each case is proven to be superintegrable, and explicit solutions are given.

Spherical HarmonicsYlm(θ,ϕ): Positive and Negative Integer Representations ofsu(1,1)forl-mandl+m

The azimuthal and magnetic quantum numbers of spherical harmonicsYlm(θ,ϕ)describe quantization corresponding to the magnitude andz-component of angular momentum operator in the framework of realization ofsu(2)Lie algebra symmetry. The azimuthal quantum numberlallocates to itself an additional ladder symmetry by the operators which are written in terms ofl. Here, it is shown that simultaneous realization of both symmetries inherits the positive and negative(l-m)- and(l+m)-integer discrete irreducible representations forsu(1,1)Lie algebra via the spherical harmonics on the sphere as a compact manifold. So, in addition to realizing the unitary irreducible representation ofsu(2)compact Lie algebra via theYlm(θ,ϕ)’s for a givenl, we can also representsu(1,1)noncompact Lie algebra by spherical harmonics for given values ofl-mandl+m.

Algebraic properties of energy raising and lowering ladder operators for the finite and infinite spectrum potential systems

An enquiry is made into the Lie algebraic property of the energy raising and lowering ladder operators for a discrete (bound state) spectrum. Starting with the most general construction of these operators in the energy representation we investigate the necessary and sufficient conditions for these operators to form a realization of su(1,1) or su(2) algebra. We formally establish the truth of the undeclared conjecture that a finite spectrum bound state system carries a realization of su(2) algebra and that an infinite spectrum bound state system carries a realization of the su(1,1) algebra. We have discussed the position space realization of these operators for some well known solvable potential systems.

Realization of theSU(N)Kondo Effect in a Strong Magnetic Field

In this Letter we suggest a realization of the SU(N) Kondo effect, using quantum dots at strong magnetic field. We propose using edge states of the quantum Hall effect as pseudospin that interact with multiple quantum dots structures. In the suggested realization one can access each pseudospin separately and hence may perform a set of experiments that were impossible until now. We focus on the realization of SU(2) and SU(3) Kondo effects and find in the unitary limit a conductivity of 3/4 quantum conductance in the SU(3) case.

A new finite-dimensional pair coherent state studied by virtue of the entangled state representation and its statistical behavior

In this paper we construct a new type of finite-dimensional pair coherent states | ξ, q〉 as realizations of SU(2) Lie algebra. Using the technique of integration within an ordered product of operator, the nonorthogonality and completeness properties of the state | ξ, q〉 are investigated. Based on the Wigner operator in the entangled state | τ〉 representation, the Wigner function of | ξ, q〉 is obtained. The properties of | ξ, q〉 are discussed in terms of the negativity of its Wigner function. The tomogram of | ξ, q〉 is calculated with the aid of the Radon transform between the Wigner operator and the projection operator of the entangled state | η, κ 1, κ 2〉. In addition, using the entangled state | τ〉 representation of | ξ, q〉 to show that the states | ξ, q〉 are just a set of energy eigenstates of time-independent two coupled oscillators.

Duality in Interacting Particle Systems and Boson Representation

In the context of Markov processes, we show a new scheme to derive dual processes and a duality function based on a boson representation. This scheme is applicable to a case in which a generator is expressed by boson creation and annihilation operators. For some stochastic processes, duality relations have been known, which connect continuous time Markov processes with discrete state space and those with continuous state space. We clarify that using a generating function approach and the Doi-Peliti method, a birth-death process (or discrete random walk model) is naturally connected to a differential equation with continuous variables, which would be interpreted as a dual Markov process. The key point in the derivation is to use bosonic coherent states as a bra state, instead of a conventional projection state. As examples, we apply the scheme to a simple birth-coagulation process and a Brownian momentum process. The generator of the Brownian momentum process is written by elements of the SU(1,1) algebra, and using a boson realization of SU(1,1) we show that the same scheme is available.

Solutions of Two-Mode Bosonic and Transformed Hamiltonians

We have constructed the quasi-exactly-solvable two-mode bosonic realization of SU(2). Two-mode boson Hamiltonian is defined through a differential equation which is solved by quantum Hamilton-Jacobi formalism. The squeezed states of two-mode boson systems are characterized through canonical transformation. The illustrated concept of squeezed boson systems has been applied two-mode bosonic Hamiltonian which is a squeezed one and is determined through a differential equation. This differential equation is solved and energy eigenvalues are found approximately.

Atiyah-Singer Index Theorem in an SO(3) Yang-Mills-Higgs System and Derivation of a Charge Quantization Condition

The Atiyah-Singer index theorem is generalized to a two-dimensional SO(3) Yang-Mills-Higgs (YMH) system. The generalized theorem is proven by using the heat kernel method and a nonlinear realization of SU(2) gauge symmetry. This theorem is applied to the problem of deriving a charge quantization condition in the four-dimensional SO(3) YMH system with non-Abelian monopoles. The resulting quantization condition, eg=n (n: integer), for an electric charge e and a magnetic charge g is consistent with that found by Arafune, Freund and Goebel. It is shown that the integer n is half of the index of a Dirac operator.

Nonlinear squeezed states for SU(1,1) Lie algebra

The nonlinear extensions of the single-mode squeezed vacuum and squeezed coherent states are studied. We have constructed the nonlinear squeezed states (NLSS's) realization of SU(1,1) Lie algebra. Two cases of this realization are considered for unitary and non-unitary deformation operator function. The nonlinear squeezed coherent states (NLSCS's) are defined and special cases of these states are obtained. Some nonclassical properties of these states are discussed. The s-parameterized characteristic function and various moments are calculated. The Glauber second-order coherence function is calculated. The squeezing properties of the NLSCS's are studied. Analytical and numerical results for the quadrature component distributions for the NLSCS's are presented. A generation scheme for NLSCS's using the trapped ions centre-of-mass motion approach is proposed.

Infinite statistics and theSU(1, 1) phase operator

A few years ago, Agarwal (1991 Phys. Rev. A 44 8398) showed that the Susskind–Glogower phase operators, expressible in terms of Bose operators, provide a realization of the algebra for particles obeying infinite statistics. In this paper we show that the SU(1, 1) phase operators, constructed in terms of the elements of the su(1, 1) Lie algebra, also provide a realization of the algebra for infinite statistics. There are many realizations of the su(1, 1) algebra in terms of single or multimode bose operators, three of which are discussed along with their corresponding phase states. The Susskind–Glogower phase operator is a special case of the SU(1, 1) phase operator associated with the Holstein–Primakoff realization of su(1, 1).

Higher-order fluctuations and SU(1,1) higher-order squeezing in SU(1,1) generalized coherent states

The higher-order fluctuations in the SU(1,1) generalized coherent states are discussed. The definition of higher-order SU(1,1) Squeezing is introduced in terms of higher-order uncertainty relation. For two possible bosonic realizations of SU(1,1) Lie algebra, the second-, fourth- and sixth-order SU(1,1) squeezing are examined in detail. It is shown that the SU(1,1) generalized coherent states can be squeezed to not only second-order, but also fourth-and sixth-order. Hence, it follows that the higher-order squeezing will occur for the fluctuations of the square of amplitude in squeezed vacuum. SU(1,1) higher-order squeezing is a kind of non-classical property which is independent of second-order squeezing.

Realization of global symmetries in the Wilsonian renormalization group

We present a method to solve the master equation for the Wilsonian action in the antifield formalism. This is based on a representation theory for cutoff dependent global symmetries along the Wilsonian renormalization group (RG) flow. For the chiral symmetry, the master equation for the free theory yields a continuum version of the Ginsparg-Wilson relation. We construct chiral invariant operators describing fermionic self-interactions. The use of canonically transformed variables is shown to simplify the underlying algebraic structure of the symmetry. We also give another non-trivial example, a realization of SU(2) vector symmetry. Our formalism may be used for a non-perturbative truncation of the Wilsonian action preserving global symmetries.

Uncorrelated two-mode SU (1,1) coherent states

We have constructed a new kind of two-mode bosonic realization of SU(1,1) Lie algebra, on the basis of which the SU(1,1) generalized coherent states in the two-mode Fock space are derived. These two-mode SU(1,1) coherent states, which are called uncorrelated two-mode SU(1,1) coherent states, include three special cases. For these states, we study the mean photon number distribution and their non-classical properties, which are photon anti-bunching, violations of Cauchy-Schwarz inequality and two-mode squeezing.

Intelligent states of the quantized radiation field associated with the Holstein-Primakoff realization of 𝔰𝔲(2)

We study the intelligent states associated with the Holstein-Primakoff realization of (2). The explicit expressions of these states in terms of the Gauss hypergeometric functions are derived and their statistical properties are investigated in detail. It is shown that in some special or asymptotic cases these states turn out to be such important states as the binomial states, number states, Glauber coherent states, squeezed coherent states, etc in quantum optics.

Coarse-grained description ofq-deformation top and t-j model

From RTT relations the integrable Hamiltonian of the trigonometric Goryachev-Chaplygin gyrostat is established, which can be reduced to the Hamiltonian of t-j model by using multi-fermion realization ofSU q(2) algebra and average-field approximation.

Realizations of U q ( su (1, 1)) by deformed quantum harmonic oscillator algebras and associated deformed Heisenberg algebras

Forsu(1, 1)-symmetric Hamiltonians of quantum mechanical systems (e.g. single-mode quantum harmonic oscillator, radial Schrodinger equation for Coulomb problem or isotropic quantum harmonic oscillator, etc.), the Heisenberg algebra of phase-space variables in two dimensions satisfy the bilinear commutation relation [ip,x]=1 (in normal units). Also there are different realizations ofsu(1, 1) by the generators of quantum harmonic oscillator algebra. We seek here the forms of deformed Heisenberg algebras (bilinear in deformedx and ip) associated with deformedsu(1, 1)-symmetric Hamiltonians. These forms are not unique in contrast to the undeformed case; and these forms are obtained here by considering different realizations of the deformedsu(1, 1) algebra by deformed oscillator algebras (satisfying different bilinear relations in deformed creation and annihilation operators), and then imposing different conditions (e.g. the deformed Heisenberg algebra of the form of the undeformed one, the form of realizations of the deformedsu(1, 1) algebra by deformed phase-space variables being the same as that ofsu(1, 1) algebra by undeformed phase-space variables, etc.), assuming linear relations between deformed phase-space variables and deformed creation-annihilation operators (as it is done in the undeformed case), we get different Heisenberg algebras. These facts are revealed in the case of a two-body Calogero model in its centre of mass frame (and for no other integrable systems in one-dimension having potential of the formV(xi − xj).

A New Treatment of a Two-Oscillator System: Application to Molecular Doubly Degenerate Vibrational Modes

We introduce a new formalism based on Schwinger"s realization of su(2) to treat a two-oscillator system. General operators and states are built using the algebraic chain u(2) ⊃ su(2) ⊃ so(2). All matrix elements are calculated. As an application of these general results we investigate the "E" vibrational modes of a molecule, the symmetry group of which is any of the classical point groups.