arXiv subjects

Tanaya Bhattacharyya

Publications and source records attributed to Tanaya Bhattacharyya.

15 recordsLinked to original sources

arXiv2014

Clusters of bound particles in a quantum integrable many-body system and number theory

We construct clusters of bound particles for a quantum integrable derivative delta-function Bose gas in one dimension. It is found that clusters of bound particles can be constructed for this Bose gas for some special values of the coupling constant, by taking the quasi-momenta associated with the corresponding Bethe state to be equidistant points on a single circle in the complex momentum plane. Interestingly, there exists a connection between the above mentioned special values of the coupling constant and some fractions belonging to the Farey sequences in number theory. This connection leads to a classification of the clusters of bound particles for the derivative delta-function Bose gas and the determination of various properties of these clusters like their size and their stability under a variation of the coupling constant.

cond-mat.stat-mech↗

arXiv2013

Clusters of bound particles in the derivative delta-function Bose gas

In this paper we discuss a novel procedure for constructing clusters of bound particles in the case of a quantum integrable derivative delta-function Bose gas in one dimension. It is shown that clusters of bound particles can be constructed for this Bose gas for some special values of the coupling constant, by taking the quasi-momenta associated with the corresponding Bethe state to be equidistant points on a single circle in the complex momentum plane. We also establish a connection between these special values of the coupling constant and some fractions belonging to the Farey sequences in number theory. This connection leads to a classification of the clusters of bound particles associated with the derivative delta-function Bose gas and allows us to study various properties of these clusters like their size and their stability under the variation of the coupling constant.

cond-mat.stat-mech↗

arXiv2009

Fermionic dual of one-dimensional bosonic particles with derivative delta function potential

We investigate the boson-fermion duality relation for the case of quantum integrable derivative $δ$-function bose gas. In particular, we find out a dual fermionic system with nonvanishing zero-range interaction for the simplest case of two bosonic particles with derivative $δ$-function interaction. The coupling constant of this dual fermionic system becomes inversely proportional to the product of the coupling constant of its bosonic counterpart and the centre-of-mass momentum of the corresponding eigenfunction.

hep-th↗

arXiv2007

A note on the spin-1/2 XXZ chain concerning its relation to the Bose gas

By considering the one-particle and two-particle scattering data of the spin-1/2 Heisenberg chain at T=0 we derive a continuum limit relating the spin chain to the 1D Bose gas. Applying this limit to the quantum transfer matrix approach of the Heisenberg chain we obtain expressions for the correlation functions of the Bose gas at arbitrary temperatures.

cond-mat.stat-mech↗

arXiv2005

Multi-band structure of the quantum bound states for a generalized nonlinear Schrodinger model

By using the method of coordinate Bethe ansatz, we study N-body bound states of a generalized nonlinear Schrodinger model having two real coupling constants c and η. It is found that such bound states exist for all possible values of c and within several nonoverlapping ranges (called bands) of η. The ranges of ηwithin each band can be determined completely using Farey sequences in number theory. We observe that N-body bound states appearing within each band can have both positive and negative values of the momentum and binding energy.

hep-th↗

arXiv2004

Quantum bound states for a derivative nonlinear Schrodinger model and number theory

A derivative nonlinear Schrodinger model is shown to support localized N-body bound states for several ranges (called bands) of the coupling constant eta. The ranges of eta within each band can be completely determined using number theoretic concepts such as Farey sequences and continued fractions. For N > 2, the N-body bound states can have both positive and negative momentum. For eta > 0, bound states with positive momentum have positive binding energy, while states with negative momentum have negative binding energy.

hep-th↗

arXiv2004

Quantum integrability of bosonic Massive Thirring model in continuum

By using a variant of the quantum inverse scattering method, commutation relations between all elements of the quantum monodromy matrix of bosonic Massive Thirring (BMT) model are obtained. Using those relations, the quantum integrability of BMT model is established and the S-matrix of two-body scattering between the corresponding quasi particles has been obtained. It is observed that for some special values of the coupling constant, there exists an upper bound on the number of quasi-particles that can form a quantum-soliton state of BMT model. We also calculate the binding energy for a N-soliton state of quantum BMT model.

hep-th↗

arXiv2004

Phase shift analysis of PT-symmetric nonhermitian extension of A_{N-1} Calogero model without confining interaction

We discuss a many-particle quantum system, which is obtained by adding some nonhermitian but PT (i.e. combined parity and time reversal) invariant interaction to the $A_{N-1}$ rational Calogero model without confining potential. This model gives rise to scattering states with continuous real spectrum. The scattering phase shift is determined through the exchange statistics parameter. We find that, unlike the case of usual Calogero model, the exclusion and exchange statistics parameter differ from each other in the presence of PT invariant interaction.

nlin.SI↗

arXiv2003

Construction of some special subsequences within a Farey sequence

Recently it has been found that some special subsequences within a Farey sequence play a crucial role in determining the ranges of coupling constant for which quantum soliton states can exist for an integrable derivative nonlinear Schrodinger model. In this article, we find a novel mapping which connects two such subsequences belonging to Farey sequences of different orders. By using this mapping, we construct an algorithm to generate all of these special subsequences within a Farey sequence. We also derive the continued fraction expansions for all the elements belonging to a subsequence and observe a close connection amongst the corresponding expansion coefficients.

math-ph↗

arXiv2003

Bound and scattering states of extended Calogero model with an additional PT invariant interaction

Here we discuss two many-particle quantum systems, which are obtained by adding some nonhermitian but PT (i.e. combined parity and time reversal) invariant interaction to the Calogero model with and without confining potential. It is shown that the energy eigenvalues are real for both of these quantum systems. For the case of extended Calogero model with confining potential, we obtain discrete bound states satisfying generalised exclusion statistics. On the other hand, the extended Calogero model without confining term gives rise to scattering states with continuous spectrum. The scattering phase shift for this case is determined through the exchange statistics parameter. We find that, unlike the case of usual Calogero model, the exclusion and exchange statistics parameter differ from each other in the presence of PT invariant interaction.

hep-th↗

arXiv2003

Exact solvability and quantum integrability of a derivative nonlinear Schrodinger model

By using a variant of quantum inverse scattering method (QISM) which is directly applicable to field theoretical systems, we derive all possible commutation relations among the operator valued elements of the monodromy matrix associated with an integrable derivative nonlinear Schrodinger (DNLS) model. From these commutation relations we obtain the exact Bethe eigenstates for the quantum conserved quantities of DNLS model. We also explicitly construct the first few quantum conserved quantities including the Hamiltonian in terms of the basic field operators of this model. It turns out that this quantum Hamiltonian has a new kind of coupling constant which is quite different from the classical one. This fact allows us to apply QISM to generate the spectrum of quantum DNLS Hamiltonian for the full range of its coupling constant.

hep-th↗

arXiv2003

Novel multi-band quantum soliton states for a derivative nonlinear Schrodinger model

We show that localized N-body soliton states exist for a quantum integrable derivative nonlinear Schrodinger model for several non-overlapping ranges (called bands) of the coupling constant η. The number of such distinct bands is given by Euler's ϕ-function which appears in the context of number theory. The ranges of ηwithin each band can also be determined completely using concepts from number theory such as Farey sequences and continued fractions. We observe that N-body soliton states appearing within each band can have both positive and negative momentum. Moreover, for all bands lying in the region η> 0, soliton states with positive momentum have positive binding energy (called bound states), while the states with negative momentum have negative binding energy (anti-bound states).

hep-th↗

arXiv2003

Jost solutions and quantum conserved quantities of an integrable derivative nonlinear Schrodinger model

We study differential and integral relations for the quantum Jost solutions associated with an integrable derivative nonlinear Schrodinger (DNLS) model. By using commutation relations between such Jost solutions and the basic field operators of DNLS model, we explicitly construct first few quantum conserved quantities of this system including its Hamiltonian. It turns out that this quantum Hamiltonian has a new kind of coupling constant which is quite different from the classical one. This modified coupling constant plays a crucial role in our comparison between the results of algebraic and coordinate Bethe ansatz for the case of DNLS model. We also find out the range of modified coupling constant for which the quantum $N$-soliton state of DNLS model has a positive binding energy.

hep-th↗

arXiv2003

Bound and anti-bound soliton states for a quantum integrable derivative nonlinear Schrodinger model

We find that localized quantum N-body soliton states exist for a derivative nonlinear Schrodinger (DNLS) model within an extended range of coupling constant (ξ_q) given by 0 < | ξ_q | < 1/\hbar \tan [π/(N-1)]. We also observe that soliton states with both positive and negative momentum can appear for a fixed value of ξ_q. Thus the chirality property of classical DNLS solitons is not preserved at the quantum level. Furthermore, it is found that the solitons with positive (negative) chirality have positive (negative) binding energy.

hep-th↗

arXiv2002

Algebraic Bethe ansatz for a quantum integrable derivative nonlinear Schrodinger model

We find that the quantum monodromy matrix associated with a derivative nonlinear Schrodinger (DNLS) model exhibits U(2) or U(1,1) symmetry depending on the sign of the related coupling constant. By using a variant of quantum inverse scattering method which is directly applicable to field theoretical models, we derive all possible commutation relations among the operator valued elements of such monodromy matrix. Thus, we obtain the commutation relation between creation and annihilation operators of quasi-particles associated with DNLS model and find out the $S$-matrix for two-body scattering. We also observe that, for some special values of the coupling constant, there exists an upper bound on the number of quasi-particles which can form a soliton state for the quantum DNLS model.

hep-th↗