598 research outputs found
New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach
New solutions for second-order intertwining relations in two-dimensional SUSY
QM are found via the repeated use of the first order supersymmetrical
transformations with intermediate constant unitary rotation. Potentials
obtained by this method - two-dimensional generalized P\"oschl-Teller
potentials - appear to be shape-invariant. The recently proposed method of
separation of variables is implemented to obtain a part of their
spectra, including the ground state. Explicit expressions for energy
eigenvalues and corresponding normalizable eigenfunctions are given in analytic
form. Intertwining relations of higher orders are discussed.Comment: 21 pages. Some typos corrected; imrovements added in Subsect.4.2;
some references adde
Multiparticle SUSY quantum mechanics and the representations of permutation group
The method of multidimensional SUSY Quantum Mechanics is applied to the
investigation of supersymmetrical N-particle systems on a line for the case of
separable center-of-mass motion. New decompositions of the superhamiltonian
into block-diagonal form with elementary matrix components are constructed.
Matrices of coefficients of these minimal blocks are shown to coincide with
matrices of irreducible representations of permutations group S_N, which
correspond to the Young tableaux (N-M,1^M). The connections with known
generalizations of N-particle Calogero and Sutherland models are established.Comment: 20 pages, Latex,no figure
Nonlinear supersymmetry: from classical to quantum mechanics
Quantization of the nonlinear supersymmetry faces a problem of a quantum
anomaly. For some classes of superpotentials, the integrals of motion admit the
corrections guaranteeing the preservation of the nonlinear supersymmetry at the
quantum level. With an example of the system realizing the nonlinear
superconformal symmetry, we discuss the nature of such corrections and
speculate on their possible general origin.Comment: 11 page
Motion of a spin 1/2 particle in shape invariant scalar and magnetic fields
We study the motion of a spin 1/2 particle in a scalar as well as a magnetic
field within the framework of supersymmetric quantum mechanics(SUSYQM). We also
introduce the concept of shape invariant scalar and magnetic fields and it is
shown that the problem admits exact analytical solutions when such fields are
considered.Comment: 14 page
Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
We examine the completeness of bi-orthogonal sets of eigenfunctions for
non-Hermitian Hamiltonians possessing a spectral singularity. The correct
resolutions of identity are constructed for delta like and smooth potentials.
Their form and the contribution of a spectral singularity depend on the class
of functions employed for physical states. With this specification there is no
obstruction to completeness originating from a spectral singularity.Comment: 25 pages, more refs adde
Supersymmetrical Separation of Variables for Scarf II Model: Partial Solvability
Recently, a new quantum model - two-dimensional generalization of the Scarf
II - was completely solved analytically by SUSY method for the integer values
of parameter. Now, the same integrable model, but with arbitrary values of
parameter, will be studied by means of supersymmetrical intertwining relations.
The Hamiltonian does not allow the conventional separation of variables, but
the supercharge operator does allow, leading to the partial solvability of the
model. This approach, which can be called as the first variant of
SUSY-separation, together with shape invariance of the model, provides
analytical calculation of the part of spectrum and corresponding wave functions
(quasi-exact-solvability). The model is shown to obey two different variants of
shape invariance which can be combined effectively in construction of energy
levels and wave functions.Comment: 6 p.p., accepted for publication in EP
Spontaneous Breaking of Lorentz Invariance
We describe how a stable effective theory in which particles of the same
fermion number attract may spontaneously break Lorentz invariance by giving
non-zero fermion number density to the vacuum (and therefore dynamically
generating a chemical potential term). This mecanism yields a finite vacuum
expectation value could relate to work on signals of Lorentz violation
in electrodynamics.Comment: revtex4, 11 pages, 5 figures; v2:references added; v3:more references
added, typos fixed, some points in sect. IV clarified; v4:even more
references added, discussion in sect. V extended; v5:replaced to match
published version (minor corrections of form
Superconformal mechanics and nonlinear supersymmetry
We show that a simple change of the classical boson-fermion coupling
constant, , , in the superconformal mechanics
model gives rise to a radical change of a symmetry: the modified classical and
quantum systems are characterized by the nonlinear superconformal symmetry. It
is generated by the four bosonic integrals which form the so(1,2) x u(1)
subalgebra, and by the 2(n+1) fermionic integrals constituting the two spin-n/2
so(1,2)-representations and anticommuting for the order n polynomials of the
even generators. We find that the modified quantum system with an integer value
of the parameter is described simultaneously by the two nonlinear
superconformal symmetries of the orders relatively shifted in odd number. For
the original quantum model with , , this means the
presence of the order 2p nonlinear superconformal symmetry in addition to the
osp(2|2) supersymmetry.Comment: 16 pages; misprints corrected, note and ref added, to appear in JHE
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