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Mikhail S. Plyushchay

Publications and source records attributed to Mikhail S. Plyushchay.

At least 55 records · Page 3Linked to original sources
arXiv2012

Extended supersymmetry of the self-isospectral crystalline and soliton chains

We study supersymmetric structure of the self-isospectral crystalline chains formed by N copies of the mutually displaced one-gap Lame systems. It is generated by the N(N-1) integrals of motion which are the first order matrix differential operators, by the same number of the nontrivial second order integrals, and by the N third order Lax integrals. We show that the structure admits distinct alternatives for a grading operator, and in dependence on its choice one of the third order matrix integrals plays either the role of the bosonic central charge or the role of the fermionic supercharge to be a square root of the spectral polynomial. Yet another peculiarity is that the set of all the second order integrals of motion generates a nonlinear sub-superalgebra. We also investigate the associated self-isospectral soliton chains, and discuss possible physical applications of the unusual extended supersymmetry.

hep-th↗
arXiv2012

Supersymmetric twisting of carbon nanotubes

We construct exactly solvable models of twisted carbon nanotubes via supersymmetry, by applying the matrix Darboux transformation. We derive the Green's function for these systems and compute the local density of states. Explicit examples of twisted carbon nanotubes are produced, where the back-scattering is suppressed and bound states are present. We find that the local density of states decreases in the regions where the bound states are localized. Dependence of bound-state energies on the asymptotic twist of the nanotubes is determined. We also show that each of the constructed unextended first order matrix systems possesses a proper nonlinear hidden supersymmetric structure with a nontrivial grading operator.

hep-th↗
arXiv2011

Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit

Some time ago, Thies et al. showed that the Gross-Neveu model with a bare mass term possesses a kink-antikink crystalline phase. Corresponding self-consistent solutions, known earlier in polymer physics, are described by a self-isospectral pair of one-gap periodic Lame potentials with a Darboux displacement depending on the bare mass. We study an unusual supersymmetry of such a second order Lame system, and show that the associated first order Bogoliubov-de Gennes Hamiltonian possesses the own nonlinear supersymmetry. The Witten index is ascertained to be zero for both of the related exotic supersymmetric structures, each of which admits several alternatives for the choice of a grading operator. A restoration of the discrete chiral symmetry at zero value of the bare mass, when the kink-antikink crystalline condensate transforms into the kink crystal, is shown to be accompanied by structural changes in both of the supersymmetries. We find that the infinite period limit may or may not change the index. We also explain the origin of the Darboux dressing phenomenon recently observed in a non-periodic self-isospectral one-gap Poschl-Teller system, which describes kink-antikink baryons of Dashen, Hasslacher and Neveu.

hep-th↗
arXiv2011

Klein tunneling in carbon nanostructures: a free particle dynamics in disguise

The absence of backscattering in metallic nanotubes as well as perfect Klein tunneling in potential barriers in graphene are the prominent electronic characteristics of carbon nanostructures. We show that the phenomena can be explained by a peculiar supersymmetry generated by a first order Hamiltonian and zero order supercharge operators. Like the supersymmetry associated with second order reflectionless finite-gap systems, it relates here the low-energy behavior of the charge carriers with the free particle dynamics.

cond-mat.mes-hall↗
arXiv2010

Supersymmetries of the spin-1/2 particle in the field of magnetic vortex, and anyons

The quantum nonrelativistic spin-1/2 planar systems in the presence of a perpendicular magnetic field are known to possess the N=2 supersymmetry. We consider such a system in the field of a magnetic vortex, and find that there are just two self-adjoint extensions of the Hamiltonian that are compatible with the standard N=2 supersymmetry. We show that only in these two cases one of the subsystems coincides with the original spinless Aharonov-Bohm model and comes accompanied by the super-partner Hamiltonian which allows a singular behavior of the wave functions. We find a family of additional, nonlocal integrals of motion and treat them together with local supercharges in the unifying framework of the tri-supersymmetry. The inclusion of the dynamical conformal symmetries leads to an infinitely generated superalgebra, that contains several representations of the superconformal osp(2|2) symmetry. We present the application of the results in the framework of the two-body model of identical anyons. The nontrivial contact interaction and the emerging N=2 linear and nonlinear supersymmetries of the anyons are discussed.

hep-th↗
arXiv2010

Supersymmetry of the planar Dirac - Deser-Jackiw-Templeton system, and of its non-relativistic limit

The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The superPoincaré symmetry emerges from the $osp(1|2)$ supersymmetry realized in terms of the deformed Heisenberg algebra underlying the construction. The non-relativistic limit yields spin 1/2 as well as new, spin 1 "Lévy-Leblond-type" equations which, together, carry an N=2 superSchrödinger symmetry. Part of the latter has its origin in the universal enveloping algebra of the superPoincaré algebra.

hep-th↗
arXiv2010

Self-isospectrality, mirror symmetry, and exotic nonlinear supersymmetry

We study supersymmetry of a self-isospectral one-gap Poschl-Teller system in the light of a mirror symmetry that is based on spatial and shift reflections. The revealed exotic, partially broken nonlinear supersymmetry admits seven alternatives for a grading operator. One of its local, first order supercharges may be identified as a Hamiltonian of an associated one-gap, non-periodic Bogoliubov-de Gennes system. The latter possesses a nonlinear supersymmetric structure, in which any of the three non-local generators of a Clifford algebra may be chosen as the grading operator. We find that the supersymmetry generators for the both systems are the Darboux-dressed integrals of a free spin-1/2 particle in the Schrodinger picture, or of a free massive Dirac particle. Nonlocal Foldy- Wouthuysen transformations are shown to be involved in the supersymmetric structure.

hep-th↗
arXiv2010

Bosons, fermions and anyons in the plane, and supersymmetry

Universal vector wave equations allowing for a unified description of anyons, and also of usual bosons and fermions in the plane are proposed. The existence of two essentially different types of anyons, based on unitary and also on non-unitary infinite-dimensional half-bounded representations of the (2+1)D Lorentz algebra is revealed. Those associated with non-unitary representations interpolate between bosons and fermions. The extended formulation of the theory includes the previously known Jackiw-Nair (JN) and Majorana-Dirac (MD) descriptions of anyons as particular cases, and allows us to compose bosons and fermions from entangled anyons. The theory admits a simple supersymmetric generalization, in which the JN and MD systems are unified in N=1 and N=2 supermultiplets. Two different non-relativistic limits of the theory are investigated. The usual one generalizes Levy-Leblond's spin 1/2 theory to arbitrary spin, as well as to anyons. The second, "Jackiw-Nair" limit (that corresponds to Inonu-Wigner contraction with both anyon spin and light velocity going to infinity), is generalized to boson/fermion fields and interpolating anyons. The resulting exotic Galilei symmetry is studied in both the non-supersymmetric and the supersymmetric cases.

hep-th↗
arXiv2010

The origin of the hidden supersymmetry

The hidden supersymmetry and related tri-supersymmetric structure of the free particle system, the Dirac delta potential problem and the Aharonov-Bohm effect (planar, bound state, and tubule models) are explained by a special nonlocal unitary transformation, which for the usual N=2 supercharges has a nature of Foldy-Wouthuysen transformation. We show that in general case, the bosonized supersymmetry of nonlocal, parity even systems emerges in the same construction, and explain the origin of the unusual N=2 supersymmetry of electron in three-dimensional parity even magnetic field. The observation extends to include the hidden superconformal symmetry.

hep-th↗
arXiv2010

Supersymmetry between Jackiw-Nair and Dirac-Majorana anyons

The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discrete series representation of the Lorentz algebra, which has fractional spin. In the Dirac-Majorana formulation the spin-1 part is replaced by the spin 1/2 planar Dirac equation. The two models are shown to belong to an N=1 supermultiplet, which carries a super-Poincare symmetry.

hep-th↗
arXiv2010

Hidden superconformal symmetry of spinless Aharonov-Bohm system

A hidden supersymmetry is revealed in the spinless Aharonov-Bohm problem. The intrinsic supersymmetric structure is shown to be intimately related with the scale symmetry. As a result, a bosonized superconformal symmetry is identified in the system. Different self-adjoint extensions of the Aharonov-Bohm problem are studied in the light of this superconformal structure and interacting anyons. Scattering problem of the original Aharonov-Bohm model is discussed in the context of the revealed supersymmetry.

hep-th↗
arXiv2009

Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system

We explain the origin and the nature of a special nonlinear supersymmetry of a reflectionless Poschl-Teller system by the Aharonov-Bohm effect for a nonrelativistic particle on the AdS_2. A key role in the supersymmetric structure appearing after reduction by a compact generator of the AdS_2 isometry is shown to be played by the discrete symmetries related to the space and time reflections in the ambient Minkowski space. We also observe that a correspondence between the two quantum non-relativistic systems is somewhat of the AdS/CFT holography nature.

hep-th↗
arXiv2009

Super-extended noncommutative Landau problem and conformal symmetry

A supersymmetric spin-1/2 particle in the noncommutative plane, subject to an arbitrary magnetic field, is considered, with particular attention paid to the homogeneous case. The system has three different phases, depending on the magnetic field. Due to supersymmetry, the boundary critical phase which separates the sub- and super-critical cases can be viewed as a reduction to the zero-energy eigensubspace. In the sub-critical phase the system is described by the superextension of exotic Newton-Hooke symmetry, combined with the conformal so(2,1) ~ su(1,1) symmetry; the latter is changed into so(3) ~ su(2) in the super-critical phase. In the critical phase the spin degrees of freedom are frozen and supersymmetry disappears.

hep-th↗
arXiv2008

Finite-gap systems, tri-supersymmetry and self-isospectrality

We show that an n-gap periodic quantum system with parity-even smooth potential admits $2^n-1$ isospectral super-extensions. Each is described by a tri-supersymmetry that originates from a higher-order differential operator of the Lax pair and two-term nonsingular decompositions of it; its local part corresponds to a spontaneously partially broken centrally extended nonlinear N=4 supersymmetry. We conjecture that any finite-gap system having antiperiodic singlet states admits a self-isospectral tri-supersymmetric extension with the partner potential to be the original one translated for a half-period. Applying the theory to a broad class of finite-gap elliptic systems described by a two-parametric associated Lame equation, our conjecture is supported by the explicit construction of the self-isospectral tri-supersymmetric pairs. We find that the spontaneously broken tri-supersymmetry of the self-isospectral periodic system is recovered in the infinite period limit.

hep-th↗
arXiv2008

Self-isospectrality, special supersymmetry, and their effect on the band structure

We study a planar model of a non-relativistic electron in periodic magnetic and electric fields that produce a 1D crystal for two spin components separated by a half-period spacing. We fit the fields to create a self-isospectral pair of finite-gap associated Lame equations shifted for a half-period, and show that the system obtained is characterized by a new type of supersymmetry. It is a special nonlinear supersymmetry generated by three commuting integrals of motion, related to the parity-odd operator of the associated Lax pair, that coherently reflects the band structure and all its peculiarities. In the infinite period limit it provides an unusual picture of supersymmetry breaking.

hep-th↗
arXiv2008

Hidden nonlinear su(2|2) superunitary symmetry of N=2 superextended 1D Dirac delta potential problem

We show that the N=2 superextended 1D quantum Dirac delta potential problem is characterized by the hidden nonlinear $su(2|2)$ superunitary symmetry. The unexpected feature of this simple supersymmetric system is that it admits three different $\mathbb Z_2$-gradings, which produce a separation of 16 integrals of motion into three different sets of 8 bosonic and 8 fermionic operators. These three different graded sets of integrals generate two different nonlinear, deformed forms of $su(2|2)$, in which the Hamiltonian plays a role of a multiplicative central charge. On the ground state, the nonlinear superalgebra is reduced to the two distinct 2D Euclidean analogs of a superextended Poincaré algebra used earlier in the literature for investigation of spontaneous supersymmetry breaking. We indicate that the observed exotic supersymmetric structure with three different $\mathbb Z_2$-gradings can be useful for the search of hidden symmetries in some other quantum systems, in particular, related to the Lamé equation.

hep-th↗
arXiv2007

Bosonized supersymmetry from the Majorana-Dirac-Staunton theory and massive higher-spin fields

We propose a (3+1)D linear set of covariant vector equations, which unify the spin 0 ``new Dirac equation'' with its spin 1/2 counterpart, proposed by Staunton. Our equations describe a spin (0,1/2) supermultiplet with different numbers of degrees of freedom in the bosonic and fermionic sectors. The translation-invariant spin deegres of freedom are carried by two copies of the Heisenberg algebra. This allows us to realize space-time supersymmetry in a bosonized form. The grading structure is provided by an internal reflection operator. Then the construction is generalized by means of the Majorana equation to a supersymmetric theory of massive higher-spin particles. The resulting theory is characterized by a nonlinear symmetry superalgebra, that, in the large-spin limit, reduces to the super-Poincare algebra with or without tensorial central charge.

hep-th↗