Schwinger Oscillator Research Articles

On the collapse revival of entanglement in a two-dimensional noncommutative harmonic oscillator: An algebraic approach

In this paper, we employ an algebraic approach to investigate the dynamics of entanglement in a two-dimensional noncommutative harmonic oscillator. We start by using the so-called the Bopp shift to convert the Hamiltonian describing the system into an equivalent commutative one. This allows us to take advantage of the Schwinger oscillator construction of [Formula: see text] Lie algebra to reveal through the time evolution operator that there is a connection between the noncommutativity and entanglement. The degree of entanglement between the states is evaluated by using the purity function. The remarkable emerging feature is that, as long as the noncommutativity parameter is nonvanishing, the system exhibits the phenomenon of collapse and revival of entanglement.

Geometric phases for finite-dimensional systems—The roles of Bargmann invariants, null phase curves, and the Schwinger–Majorana SU(2) framework

We present a study of the properties of Bargmann Invariants (BIs) and Null Phase Curves (NPCs) in the theory of the geometric phase for finite dimensional systems. A recent suggestion to exploit the Majorana theorem on symmetric SU(2) multispinors is combined with the Schwinger oscillator operator construction to develop efficient operator-based methods to handle these problems. The BI is described using intrinsic unitary invariant angle parameters whose algebraic properties as functions of Hilbert space dimension are analyzed using elegant group theoretic methods. The BI-geometric phase connection, extended by the use of NPCs, is explored in detail, and interesting new experiments in this subject are pointed out.

Deconstructing graviphoton from mass-deformed ABJM

Mass-deformed ABJM theory has a maximally supersymmetric fuzzy two-sphere vacuum solution where the scalar fields are proportional to the TGRVV matrices. We construct these matrices using Schwinger oscillators. This shows that the ABJM gauge group that corresponds to the fuzzy two-sphere geometry is $U(N)\times U(N-1)$. We deconstruct the graviphoton term in the D4 brane theory. The normalization of this term is fixed by topological reasons. This gives us the correct normalization of the deconstructed U(1) gauge field and fixes the Yang -Mills coupling constant to the value which corresponds to M5 brane compactified on $\mb{R}^ {1,2} \times S^3/{\mb{Z}_k}$. The graviphoton term also enable us to show that the zero mode contributions to the partition functions for the D4 and the M5 brane agree.

Irreducible SU(3) Schwinger bosons

We develop simple computational techniques for constructing all possible SU(3) representations in terms of irreducible SU(3) Schwinger bosons. We show that these irreducible Schwinger oscillators make SU(3) representation theory as simple as SU(2). The new Schwinger oscillators satisfy certain Sp(2,R) constraints and solve the multiplicity problem as well. These SU(3) techniques can be generalized to SU(N).

Husimi distribution for the linear rigid rotator

We find the Husimi distribution for the linear rigid rotator. The Husimi function can be viewed in a variety of ways. In particular, we obtain it as the expectation value of the density operator in a suitable basis of coherent states. We employ the Schwinger's oscillator model for the construction of the angular momentum coherent states.

Semiclassical analysis of Wigner 3j-symbol

We analyse the asymptotics of the Wigner 3j-symbol as a matrix element connecting eigenfunctions of a pair of integrable systems, obtained by lifting the problem of the addition of angular momenta into the space of Schwinger's oscillators. A novel element is the appearance of compact Lagrangian manifolds that are not tori, due to the fact that the observables defining the quantum states are noncommuting. These manifolds can be quantized by generalized Bohr–Sommerfeld rules and yield all the correct quantum numbers. The geometry of the classical angular momentum vectors emerges in a clear manner. Efficient methods for computing amplitude determinants in terms of Poisson brackets are developed and illustrated.

Exact diagonalization solution and coherent state variational method of the coupling system of carrier and ferromagnetic material

The problem of the coupling system of carrier and ferromagnetic material has been transformed into that of the coupling system of carrier and two kinds of Bosons by using Schwinger's oscillator theory of angular momentum. That the existence of bound polaron in ferromagnetic material depends on the existence of impurity potential in this material is solved exactly by diagonalization and the conclusion obtained is in agreement with the general view point of other works. The values of the energy of ground state obtained by the exact solution and coherent state variation method is agree quite well.The qualitative characters of state vector given by both methods are consistent. The results shows that the coherent state variation method is valid and precise enough for this problem. Exact solution method will provide a basis to check the validity of any other approximate methods.

THE SCHWINGER REPRESENTATION OF A GROUP: CONCEPT AND APPLICATIONS

The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the Schwinger oscillator construction for SU(2), and its relevance in several quantum mechanical contexts is highlighted. The Schwinger representations for SU(2), SO(3) and SU(n) for all n are constructed via specific carrier spaces and group actions. In the SU(2) case, connections to the oscillator construction and to Majorana's theorem on pure states for any spin are worked out. The role of the Schwinger Representation in setting up the Wigner–Weyl isomorphism for quantum mechanics on a compact simple Lie group is brought out.

Kernel solutions of the Kostant operator on eight-dimensional quotient spaces

After introducing the generators and irreducible representations of the su(5) and so(6) Lie algebras in terms of the Schwinger's oscillators, the general kernel solutions of the Kostant operators on eight-dimensional quotient spaces su(5)/su(4) × u(1) and so(6)/so(4) × so(2) are derived in terms of the diagonal subalgebras su(4) × u(1) and so(4) × so(2), respectively.

The Schwinger SU(3) construction. I. Multiplicity problem and relation to induced representations

The Schwinger oscillator operator representation of SU(3) is analyzed with particular reference to the problem of multiplicity of irreducible representations. It is shown that with the use of an Sp(2,R) unitary representation commuting with the SU(3) representation, the infinity of occurrences of each SU(3) irreducible representation can be handled in complete detail. A natural “generating representation” for SU(3), containing each irreducible representation exactly once, is identified within a subspace of the Schwinger construction, and this is shown to be equivalent to an induced representation of SU(3).

The Schwinger SU(3) construction. II. Relations between Heisenberg–Weyl and SU(3) coherent states

The Schwinger oscillator operator representation of SU(3), studied in a previous paper from the representation theory point of view, is analyzed to discuss the intimate relationships between standard oscillator coherent state systems and systems of SU(3) coherent states. Both SU(3) standard coherent states, based on choice of highest weight vector as fiducial vector, and certain other specific systems of generalized coherent states, are found to be relevant. A complete analysis is presented, covering all the oscillator coherent states without exception, and amounting to SU(3) harmonic analysis of these states.

A coherent understanding of solvable models for quantum measurement processes

By making use of Schwinger's oscillator model of angular momentum, we put forward an interesting connection among three solvable Hamiltonians, widely used for discussions on the quantum measurement problem. This connection implies that a particular macroscopic limit has to be taken for these models to be physically sensible.