arXiv subjects

Vivek M. Vyas

Publications and source records attributed to Vivek M. Vyas.

At least 19 recordsLinked to original sources

arXiv2025

Topological aspects of periodically driven non-Hermitian Su-Schrieffer-Heeger model

A non-Hermitian generalization of the Su-Schrieffer-Heeger model driven by a periodic external potential is investigated, and its topological features are explored. We find that the bi-orthonormal geometric phase acts as a topological index, well capturing the presence/absence of the zero modes. The model is observed to display trivial and non-trivial insulator phases and a topologically non-trivial M${ö}$bius metallic phase. The driving field amplitude is shown to be a control parameter causing topological phase transitions in this model. While the system displays zero modes in the metallic phase apart from the non-trivial insulator phase, the metallic zero modes are not robust, as the ones found in the insulating phase. We further find that zero modes' energy converges slowly to zero as a function of the number of dimers in the M${ö}$bius metallic phase compared to the non-trivial insulating phase.

cond-mat.mes-hall↗

arXiv2025

Generalised Geometric Phase

A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown. An appreciation of fact that the interference phenomenon also manifests in the average of an observable, allows us to define the argument of the matrix element of an observable as a generalised relative phase. This identification naturally paves the way for defining an operator generalisation of the geometric phase following Pancharatnam. The notion of natural connection finds an appropriate operator generalisation, and the generalised geometric phase is indeed found to be the (an)holonomy of the generalised connection. It is shown that in scenarios wherein the usual geometric phase is not defined, the generalised geometric phase manifests as a global phase acquired by a quantum state in course of time evolution. The generalised geometric phase is found to contribute to the shift in the energy spectrum due perturbation, and to the forward scattering amplitude in a scattering problem.

quant-ph↗

arXiv2025

Coherent States in Classical Field Theory

We illustrate the emergence of classical analogue of coherent state and its generalisation in a purely classical field theoretical setting. Our algebraic approach makes use of the Poisson bracket and symmetries of the underlying field theory, in a complete parallel to the quantum construction. The classical phase space picture is found to play a key role in this construction.

hep-th↗

arXiv2023

Generalised Geometric Phase: Mathematical Aspects

An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum systems. While probing the average of any observable it is found that a quantum system exhibits different ray spaces and associated fibre bundle structures. The generalised geometric phase is understood as (an)holonomy of a connection over these fibre bundles. The underlying ray spaces in general are found to be pseudo-Kahler manifolds, and its symplectic structure gets manifests as the generalised geometric phase.

quant-ph↗

arXiv2022

Response to the comment on "Do Bloch waves interfere with one another ?"

Here a generalised argument showing the existence of the Bloch superselection rule is presented, in response to the recent comment by Sowinski. In light of the role played by the periodic boundary condition, locality and topology in the system, the claim made in the comment is found untenable.

quant-ph↗

arXiv2022

Pancharatnam-Zak phase

Three decades ago, in a celebrated work, Zak found an expression for the geometric phase acquired by an electron in a one-dimensional periodic lattice as it traverses the Bloch band. Such a geometric phase is useful in characterizing the topological properties and the electric polarization of the periodic system. Unfortunately Zak's expression suffers from two flaws: its value depends upon the choice of origin of the unit cell, and is gauge dependent. Here we explain that these flaws in Zak's expression arise from the assumption that the electron's adiabatic motion is cyclic in the sense of recurrence of the density matrix in course of time evolution. We find through a careful investigation that the system displays cyclicity in a generalized sense wherein the physical observables return in the course of evolution. This notion of generalized cyclicity paves the way for a correct and consistent expression for the geometric phase in this system, christened as Pancharatnam-Zak phase. Pancharatnam-Zak geometric phase does not suffer from the flaws inherent in Zak's expression, and correctly classifies the Bloch bands of the lattice. A natural filled band extension of the Pancharatnam-Zak phase is also constructed and studied.

quant-ph↗

arXiv2021

Do Bloch waves interfere with one another ?

Here we show that two Bloch states, which are energy eigenstates of a quantum periodic potential problem, with different wavevectors can not be linearly superposed to display quantum interference of any kind that captures the relative phase between them. This is due to the existence of a superselection rule in these systems, whose origin lies in the discrete translation symmetry. A topological reason leading to such a superselection is found. A temporal analogue of this superselection rule in periodically driven quantum systems is also uncovered, which forbids the coherent superposition of any two quasi-periodic Floquet states with different quasienergies.

quant-ph↗

arXiv2019

Some results on topological currents in field theory

A few exact results concerning topological currents in field theories are obtained. It is generally shown that, a topological charge can not generate any kind of symmetry transformation on the fields. It is also proven that, the existence of a charge that does not generate any kind of symmetry transformation on the fields, has to be of topological origin. As a consequence, it is found that in a given theory, superconductivity via Anderson-Higgs route can only occur if the gauge coupling with other fields is minimal. Several physical implications of these results are studied.

hep-th↗

arXiv2018

Airy wavepackets are Perelomov coherent states

Accelerating non-spreading wavepackets in nonrelativistic free particle system, with probability distribution having an Airy function profile, were discovered by Berry and Balazs (1979), and have been subsequently realised in several optical experiments. It is shown that these wavepackets are actually Perelomov coherent states. It is found that the Galilean invariance of the Schrodinger equation plays a key role in making these states unique and giving rise to their unusual propagation properties.

quant-ph↗

arXiv2018

Density wave ground state and fractional fermions in LaAlO3/SrTiO3 heterostructure

We show that the non-homogeneous charged layer distribution of the LaAlO 3 /SrT iO 3 heterostructure undergoing interface reconstruction is the density wave ground state of the well known anharmonic lattice model described by the λϕ 4 continuum model. The two dimensional planar structure of the charged surfaces with alternating polarity leads to an effective one dimensional model, with fermions coupled to the planar distortions acting as long wavelength optical phonons in one dimension. The Hamiltonian with the desired anharmonicity for describing the non-homogeneous density wave type distortion is the same one that describes the fermion number fractionalization in polyacetylene. The general solution of this theory is the Jacobi elliptic sine function sn(x;k), which in the limiting case of lattice distortion being localized gives the kink/anti-kink solution.

cond-mat.mtrl-sci↗

arXiv2017

Light-matter interaction and Bose-Einstein condensation of light

The atom - electromagnetic field interaction is studied in the Dicke model, wherein a single field mode is interacting with a collection of two level atoms at thermal equilibrium. It is found that in the superradiant phase of the system, wherein the Bose-Einstein condensation of photons takes place, the notion of photon as an elementary electromagnetic excitation ceases to exist. The phase and intensity excitations of the condensate are found to be the true excitations of electromagnetic field. It is found that in this phase, the atom interacts with these excitations in a distinct coherent transition process, apart from the known stimulated emission/absorption and spontaneous emission processes. In the coherent transition it is found that while the atomic state changes in course of the transition process, the state of electromagnetic field remains unaffected. It is found that the transition probability of such coherent transition process is macroscopically large compared to other stimulated emission/absorption and spontaneous emission processes.

physics.optics↗

arXiv2017

Photon mass via current confinement

A parity invariant theory, consisting of two massive Dirac fields, defined in three dimensional space-time, with the confinement of a certain current is studied. It is found that the electromagnetic field, when coupled minimally to these Dirac fields, becomes massive owing to the current confinement. It is seen that the origin of photon mass is not due to any kind of spontaneous symmetry breaking, but only due to current confinement.

hep-th↗

arXiv2015

Quantum theory of nonlocal nonlinear Schrodinger equation

Nonlocal nonlinear Schrodinger model is quantised and exactly solved using the canonical framework. It is found that the usual canonical quantisation of the model leads to a theory with pathological inner product. This problem is resolved by constructing another inner product over the vector space of the theory. The resultant theory is found to be identical to that of nonrelativistic bosons with delta function interaction potential, devoid of any nonlocality. The exact eigenstates are found using the Bethe ansatz technique.

quant-ph↗

arXiv2015

A gauge theory of massive spin one particles

An Abelian gauge theory describing dynamics of massive spin one bosons is constructed. This is achieved by appending to the Maxwell action, a gauge invariant mass term. The theory is quantised in temporal as well as Lorentz gauge, and the corresponding Hilbert spaces are constructed. In both the gauges, it is found that, the theory respects Lorentz invariance, locality, causality and unitarity.

hep-th↗

arXiv2015

Generalized gauge transformation approach to construct dark solitons of coupled nonlinear Schrodinger type equations

We harness the freedom in the celebrated gauge transformation approach to generate dark solitons of coupled nonlinear Schrödinger (NLS) type equations. The new approach which is purely algebraic could prove to be very useful, particularly in the construction of vector dark solitons in the fields of nonlinear optics, plasma physics and Bose-Einstein condensates. We have employed this algebraic method to coupled Gross- Pitaevskii (GP) and NLS equations and obtained dark solitons.

nlin.SI↗

arXiv2014

A method to solve nonlinear Schrödinger equation using Riccati equation

A method to find exact solutions to nonlinear Schrödinger equation, defined on a line and on a plane, is found by connecting it with second order linear ordinary differential equation. The connection is essentially made using Riccati equation. Generalisation of several known solutions is found using this method, in case of nonlinear Schrödinger equation defined on a line. This method also yields non-singular and singular vortex solutions, when applied to nonlinear Schrödinger equation on a plane.

nlin.SI↗

arXiv2014

Rogue solitons in Heisenberg spin chain

Following the connection of the non-linear Schrödinger equation with the continuum Heisenberg spin chain, we find the rogue soliton equivalent in the spin system. The breathers are also mapped to the corresponding space or time localized oscillatory modes, through the moving curve analogy. The spatio-temporal evolution of the curvature and torsion of the curve, underlying these dynamical systems, are explicated to illustrate the localization property of the rogue waves.

nlin.PS↗

arXiv2013

On Berezinskii-Kosterlitz-Thouless phase transition and universal breathing mode in two dimensional photon gas

A system of two dimensional photon gas has recently been realized experimentally. It is pointed out that this setup can be used to observe a universal breathing mode of photon gas. It is shown that a modification in the experimental setup would open up a possibility of observing the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in such a system. It is shown that the universal jump in the superfluid density of light in the output channel can be used as an unambiguous signature for the experimental verification of the BKT transition.

physics.optics↗