arXiv subjects

Avadh Saxena

Publications and source records attributed to Avadh Saxena.

At least 109 records · Page 6Linked to original sources

arXiv2016

Nonlinear Dirac equation solitary waves under a spinor force with different components

We consider the nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar self-interaction in the presence of external forces as well as damping of the form $γ^0 f(x,t) - i μγ^0 Ψ$, where both $f, \{f_j = r_i e^{i K_j x} \}$ and $Ψ$ are two-component spinors. We develop an approximate variational approach using collective coordinates (CC) for studying the time dependent response of the solitary waves to these external forces. In our previous paper we assumed $K_j=K, ~ j=1,2$ which allowed a transformation to a simplifying coordinate system, and we also assumed the "small" component of the external force was zero. Here we include the effects of the small component and also the case $K_1 \neq K_2$ which dramatically modifies the behavior of the solitary wave in the presence of these external forces.

nlin.PS↗

arXiv2016

Helicoidal Graphene Nanoribbons: Chiraltronics

We present a calculation of the effective geometry-induced quantum potential for the carriers in graphene shaped as a helicoidal nanoribbon. In this geometry the twist of the nanoribbon plays the role of an effective transverse electric field in graphene and this is reminiscent of the Hall effect. However, this effective electric field has a different sign for the two iso-spin states and translates into a mechanism to separate the two chiral species on the opposing rims of the nanoribbon. Iso-spin transitions are expected with the emission or absorption of microwave radiation which could be adjusted to be in the THz region.

cond-mat.mes-hall↗

arXiv2016

$\mathcal{P}\mathcal{T}$-symmetric slowing-down of decoherence

We investigate $\mathcal{P}\mathcal{T}$-symmetric quantum systems ultra-weakly coupled to an environment. We find that such open systems evolve under $\mathcal{P}\mathcal{T}$-symmetric, purely dephasing and unital dynamics. The dynamical map describing the evolution is then determined explicitly using a quantum canonical transformation. Furthermore, we provide an explanation of why $\mathcal{P}\mathcal{T}$-symmetric dephasing type interactions lead to \emph{critical slowing down of decoherence}. This effect is further exemplified with an experimentally relevant system -- a $\mathcal{P}\mathcal{T}$-symmetric qubit easily realizable, \emph{e.g.}, in optical or microcavity experiments.

quant-ph↗

arXiv2016

Variational Approach to studying solitary waves in the nonlinear Schrodinger equation with Complex Potentials

We discuss the behavior of solitary wave solutions of the nonlinear Schr{ö}dinger equation (NLSE) as they interact with complex potentials, using a four parameter variational approximation based on a dissipation functional formulation of the dynamics. We concentrate on spatially periodic potentials with the periods of the real and imaginary part being either the same or different. Our results for the time evolution of the collective coordinates of our variational ansatz are in good agreement with direct numerical simulation of the NLSE. We compare our method with a collective coordinate approach of Kominis and give examples where the two methods give qualitatively different answers. In our variational approach, we are able to give analytic results for the small oscillation frequency of the solitary wave oscillating parameters which agree with the numerical solution of the collective coordinate equations. We also verify that instabilities set in when the slope of $dp(t)/dv(t)$ becomes negative when plotted parametrically as a function of time, where $p(t)$ is the momentum of the solitary wave and $v(t)$ the velocity.

nlin.PS↗

arXiv2016

Stability of exact solutions of the nonlinear Schroedinger equation in an external potential having supersymmetry and parity-time symmetry

We discuss the stability properties of the solutions of the general nonlinear Schroedinger equation (NLSE) in 1+1 dimensions in an external potential derivable from a parity-time (PT) symmetric superpotential $W(x)$ that we considered earlier [Kevrekedis et al Phys. Rev. E 92, 042901 (2015)]. In particular we consider the nonlinear partial differential equation $\{ i \partial_t + \partial_x^2 - V^{-}(x) +| ψ(x,t) |^{2κ} \} \, ψ(x,t) = 0$, for arbitrary nonlinearity parameter $κ$. We study the bound state solutions when $V^{-}(x) = (1/4- b^2)$ sech$^2(x)$, which can be derived from two different superpotentials $W(x)$, one of which is complex and $PT$ symmetric. Using Derrick's theorem, as well as a time dependent variational approximation, we derive exact analytic results for the domain of stability of the trapped solution as a function of the depth $b^2$ of the external potential. We compare the regime of stability found from these analytic approaches with a numerical linear stability analysis using a variant of the Vakhitov-Kolokolov (V-K) stability criterion. The numerical results of applying the V-K condition give the same answer for the domain of stability as the analytic result obtained from applying Derrick's theorem. Our main result is that for $κ>2$ a new regime of stability for the exact solutions appears as long as $b > b_{crit}$, where $b_{crit}$ is a function of the nonlinearity parameter $κ$. In the absence of the potential the related solitary wave solutions of the NLSE are unstable for $κ>2$.

nlin.PS↗

arXiv2016

Approximate Analytic Solutions to Coupled Nonlinear Dirac Equations

We consider the coupled nonlinear Dirac equations (NLDE's) in 1+1 dimensions with scalar-scalar self interactions $\frac{ g_1^2}{2} ( {\bpsi} ψ)^2 + \frac{ g_2^2}{2} ( {\bphi} ϕ)^2 + g_3^2 ({\bpsi} ψ) ( {\bphi} ϕ)$ as well as vector-vector interactions of the form $\frac{g_1^2 }{2} (\bpsi γ_μ ψ)(\bpsi γ^μ ψ)+ \frac{g_2^2 }{2} (\bphi γ_μ ϕ)(\bphi γ^μ ϕ) + g_3^2 (\bpsi γ_μ ψ)(\bphi γ^μ ϕ). $ Writing the two components of the assumed solitary wave solution of these equations in the form $ψ= e^{-i ω_1 t} \{R_1 \cos θ, R_1 \sin θ\}$, $ϕ= e^{-i ω_2 t} \{R_2 \cos η, R_2\sin η\}$, and assuming that $ θ(x),η(x)$ have the {\it same} functional form they had when $g_3$=0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for $R_i(x)$ which are valid for small values of $g_3^2/ g_2^2 $ and $g_3^2/ g_1^2$. In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schrödinger equation for which we obtain two exact pulse solutions vanishing at $x \rightarrow \pm \infty$.

nlin.PS↗

arXiv2016

Repeatability of measurements: Equivalence of hermitian and non-hermitian observables

A non-commuting measurement transfers, via the apparatus, information encoded in a system's state to the external "observer". Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Therefore, even a possibility to describe physical reality by means of non-hermitian operators should \emph{volens nolens} be excluded as their eigenstates are not orthogonal. Here, we show that non-hermitian operators with real spectrum can be treated within the standard framework of quantum mechanics. Furthermore, we propose a quantum canonical transformation that maps hermitian systems onto non-hermitian ones. Similar to classical inertial forces this transformation is accompanied by an energetic cost pinning the system on the unitary path.

quant-ph↗

arXiv2016

Non-hermitian quantum thermodynamics

Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal processes arbitrarily far from equilibrium. In the quasistatic limit however, the second law leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Furthermore, we propose two setups to test our predictions. Namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model.

quant-ph↗

arXiv2016

Dynamics of Dirac strings and monopole-like excitations in chiral magnets under a current drive

Skyrmion lines in metallic chiral magnets carry an emergent magnetic field experienced by the conduction electrons. The inflow and outflow of this field across a closed surface is not necessarily equal, thus it allows for the existence of emergent monopoles. One example is a segment of skyrmion line inside a crystal, where a monopole and antimonopole pair is connected by the emergent magnetic flux line. This is a realization of Dirac string-like excitations. Here we study the dynamics of monopoles in chiral magnets under an electric current. We show that in the process of creation of skyrmion lines, skyrmion line segments are first created via the proliferation of monopoles and antimonopoles. Then these line segments join and span the whole system through the annihilation of monopoles. The skyrmion lines are destroyed via the proliferation of monopoles and antimonopoles at high currents, resulting in a chiral liquid phase. We also propose to create the monopoles in a controlled way by applying an inhomogenous current to a crystal. Remarkably, an electric field component in the magnetic field direction proportional to the current squared in the low current region is induced by the motion of distorted skyrmion lines, in addition to the Hall and longitudinal voltage. The existence of monopoles can be inferred from transport or imaging measurements.

cond-mat.str-el↗

arXiv2016

Novel PT-invariant Kink and Pulse Solutions For a Large Number of Real Nonlinear Equations

For a large number of real nonlinear equations, either continuous or discrete, integrable or nonintegrable, uncoupled or coupled, we show that whenever a real nonlinear equation admits kink solutions in terms of $\tanh βx$, where $β$ is the inverse of the kink width, it also admits solutions in terms of the PT-invariant combinations $\tanh 2βx \pm i \sech 2 βx$, i.e. the kink width is reduced by half to that of the real kink solution. We show that both the kink and the PT-invariant kink are linearly stable and obtain expressions for the zero mode in the case of several PT-invariant kink solutions. Further, for a number of real nonlinear equations we show that whenever a nonlinear equation admits periodic kink solutions in terms of $\sn(x,m)$, it also admits periodic solutions in terms of the PT-invariant combinations $\sn(x,m) \pm i \cn(x,m)$ as well as $\sn(x,m)\pm i \dn(x,m)$. Finally, for coupled equations we show that one cannot only have complex PT-invariant solutions with PT eigenvalue $+1$ or $-1$ in both the fields but one can also have solutions with PT eigenvalue $+1$ in one field and $-1$ in the other field.

nlin.PS↗

arXiv2015

Excitonic effects in two-dimensional semiconductors: Path integral Monte Carlo approach

One of the most striking features of novel 2D semiconductors (e.g., transition metal dichalcogenide monolayers or phosphorene) is a strong Coulomb interaction between charge carriers resulting in large excitonic effects. In particular, this leads to the formation of multi-carrier bound states upon photoexcitation (e.g., excitons, trions and biexcitons), which could remain stable at near-room temperatures and contribute significantly to optical properties of such materials. In the present work we have used the Path Integral Monte Carlo methodology to numerically study properties of multi-carrier bound states in 2D semiconductors. Specifically, we have accurately investigated and tabulated the dependence of single exciton, trion and biexciton binding energies on the strength of dielectric screening, including the limiting cases of very strong and very weak screening. The results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models.

cond-mat.mes-hall↗

arXiv2015

Reply to the Comment by Zhang and Li [J. Math. Phys. 56, 084101, 2015] on the Paper [J. Math. Phys. {\bf 56}, 032104, 2015]}

In a recent paper Zhang and Li have doubted our claim that whenever a nonlinear equation has solutions in terms of the Jacobi elliptic functions $\cn(x,m)$ and $\dn(x,m)$, then the same nonlinear equation will necessarily also have solutions in terms of $\dn(x,m) \pm \sqrt{m} \cn(x,m)$. We point out the flaw in their argument and show why our assertion is indeed valid.

nlin.PS↗

arXiv2015

More Opportunities than Wealth: A Network of Power and Frustration

We introduce a minimal agent-based model to qualitatively conceptualize the allocation of limited wealth among more abundant opportunities. We study the interplay of power, satisfaction and frustration in distribution, concentration, and inequality of wealth. Our framework allows us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from, or lose wealth to, anybody else invariably leads to a complete polarization of the distribution of wealth vs. opportunity. The picture is however dramatically modified when hard constraints are imposed over agents, and they are limited to share wealth with neighbors on a network. We then propose an out of equilibrium dynamics {\it of} the networks, based on a competition between power and frustration in the decision-making of agents that leads to network coevolution. We show that the ratio of power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of the indices of equality. The interplay of power and frustration leads to the emergence of three self-organized social classes, lower, middle, and upper class, whose interactions drive a cyclical regime.

physics.soc-ph↗

arXiv2015

Integrable and Superintegrable Klein-Gordon and Schrödinger Type Dimers

A $PT$-symmetric dimer is a two-site nonlinear oscillator or a nonlinear Schrödinger dimer where one site loses and the other site gains energy at the same rate. We present a wide class of integrable oscillator type dimers whose Hamiltonian is of arbitrary even order. Further, we also present a wide class of integrable and superintegrable nonlinear Schrödinger type dimers where again the Hamiltonian is of arbitrary even order.

nlin.SI↗

arXiv2015

Solitary waves of a PT-symmetric Nonlinear Dirac equation

In the present work, we consider a prototypical example of a PT-symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the PT-phase transition in an analytical form. We then focus on the examination of the nonlinear model. We consider the continuation in the PT-symmetric model of the solutions of the corresponding Hamiltonian model and find that the solutions can be continued robustly as stable ones all the way up to the PT-transition threshold. In the latter, they degenerate into linear waves. We also examine the dynamics of the model. Given the stability of the waveforms in the PT-exact phase we consider them as initial conditions for parameters outside of that phase. We find that both oscillatory dynamics and exponential growth may arise, depending on the size of the corresponding "quench". The former can be characterized by an interesting form of bi-frequency solutions that have been predicted on the basis of the SU(1,1) symmetry. Finally, we explore some special, analytically tractable, but not PT-symmetric solutions in the massless limit of the model.

nlin.PS↗

arXiv2015

Quantum work statistics of charged Dirac particles in time-dependent fields

The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the conceptual framework we solve a pedagogical, yet experimentally relevant, system analytically. As a main result we obtain the exact quantum work distributions for charged particles traveling through a time-dependent vector potential evolving under Schrödinger as well as under Dirac dynamics, and for which the Jarzynski equality is verified. Special emphasis is put on the conceptual and technical subtleties arising from relativistic quantum mechanics.

cond-mat.stat-mech↗

arXiv2015

PT-symmetric phase in kagome photonic lattices

Kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing $\mathcal{PT}$-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a $\mathcal{PT}$-symmetric phase for finite gain/loss parameter up to a critical value. The beam evolution in this complex kagome waveguide array exhibits a novel oscillatory rotation of optical power along the propagation distance. Long-lived local chiral structures originating from the nearly flat bands of the kagome structure are observed when the lattice is subject to a narrow beam excitation.

physics.optics↗

arXiv2015

Novel PT-invariant Solutions For a Large Number of Real Nonlinear Equations

For a large number of real nonlinear equations, either continuous or discrete, integrable or nonintegrable, we show that whenever a real nonlinear equation admits a solution in terms of $\sech x$, it also admits solutions in terms of the PT-invariant combinations $\sech x \pm i \tanh x$. Further, for a number of real nonlinear equations we show that whenever a nonlinear equation admits a solution in terms $\sech^2 x$, it also admits solutions in terms of the PT-invariant combinations $\sech^2 x \pm i \sech x \tanh x$. Besides, we show that similar results are also true in the periodic case involving Jacobi elliptic functions.

nlin.SI↗