arXiv subjects

Debabrata Biswas

Publications and source records attributed to Debabrata Biswas.

At least 55 records · Page 3Linked to original sources

arXiv2013

Synchronization in hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment

The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system can show in-phase or complete synchronization, and also inverse-phase or anti-synchronization. This paper reports the first experimental confirmation of synchronization of hyperchaos in time-delayed electronic oscillators coupled indirectly through a common environment. We confirm the occurrence of in-phase and inverse-phase synchronization phenomena in the coupled system through the dynamical measures like generalized autocorrelation function, correlation of probability of recurrence, and the concept of localized sets computed directly from the experimental time-series data. We also present a linear stability analysis of the coupled system. The experimental and analytical results are further supported by the detailed numerical analysis of the coupled system. Apart from the above mentioned measures, we numerically compute another quantitative measure, namely, Lyapunov exponent spectrum of the coupled system that confirms the transition from the in-phase (inverse-phase) synchronized state to the complete (anti-) synchronized state with the increasing coupling strength.

nlin.CD↗

arXiv2012

Comment on "New Scaling of Child-Langmuir Law in the Quantum Regime"

In their letter on the quantum Child-Langmuir law, Ang, Kwan and Lau (Phys. Rev. Lett. 91, 208303 (2003)) include exchange correlation effects within the Kohn-Sham density functional theory and explore numerically the maximum transmitted current in nanogaps. We show here that the calculations are in error as the exchange-correlation component of the chemical potential has been ignored while fixing the boundary conditions for the Hartree potential.

cond-mat.mes-hall↗

arXiv2011

Transport across nanogaps using semiclassically consistent boundary conditions

Charge particle transport across nanogaps is studied theoretically within the Schrodinger-Poisson mean field framework and the existence of limiting current investigated. It is shown that the choice of a first order WKB wavefunction as the transmitted wave leads to self consistent boundary conditions and gives results that are significantly different in the non-classical regime from those obtained using a plane transmitted wave. At zero injection energies, the quantum limiting current density, J_c, is found to obey the local scaling law J_c ~ (V_g)^alpha/(D)^{5-2alpha} with the gap separation D and voltage V_g. The exponent alpha > 1.1 with alpha --> 3/2 in the classical regime of small de Broglie wavelengths. These results are consistent with recent experiments using nanogaps most of which are found to be in a parameter regime where classical space charge limited scaling holds away from the emission dominated regime.

cond-mat.mes-hall↗

arXiv2007

Evolving momentum-projected densities in billiards with quantum states

The classical Liouville density on the constant energy surface reveals a number of interesting features when the initial density has no directional preference. It has been shown (Physical Review Letters, 93 (2004) 204102) that the eigenvalues and eigenfunctions of the momentum-projected density evolution operator have a correspondence with the quantum Neumann energy eigenstates in billiard systems. While the classical eigenfunctions are well approximated by the quantum Neumann eigenfunctions, the classical eigenvalues are of the form f(\sqrt{E_n} vt) where {E_n} are close to the quantum Neumann eigenvalues and v is the speed of the classical particle. Despite the approximate nature of the correspondence, we demonstrate here that the exact quantum Neumann eigenstates can be used to expand and evolve an arbitrary classical density on the energy surface projected on to the configuration space. For the rectangular and stadium billiards, results are compared with the actual evolution of the density using classical trajectories.

nlin.CD↗

arXiv2006

Relation between space charge limited current and power loss in open drift tubes

Drift space is a region free from externally applied fields. It is an important part of many devices involving charged particle beams. The space charge effect imposes a limit on the current that can be transported through a drift space. A reasonable estimate of the space charge limited current density (J_{SCL}^{c}) in 'closed' drift tubes can be obtained from electrostatic considerations despite the fact that charge particle transport results in electromagnetic radiation. We deal here with the situation where the drift tube is 'open' to electromagnetic radiation, for instance due to the presence of a dielectric window. In such cases, electromagnetic radiation leaks out of the window which results in a decrease in the average kinetic energy of electrons. If the injected current density is much lower than J_{SCL}^{c}, power loss does not result in a change in the transmitted current. As the injected current density is increased, power loss increases and at a critical value lower than J_{SCL}^{c}, reflection of electrons begins to occur. We also show that the lowering of the space charge limited current on account of power loss can be incorporated in the standard electrostatic picture by introducing an effective voltage for the collection plate.

physics.plasm-ph↗

arXiv2005

Power loss in open cavity diodes and a modified Child Langmuir Law

Diodes used in most high power devices are inherently open. It is shown that under such circumstances, there is a loss of electromagnetic radiation leading to a lower critical current as compared to closed diodes. The power loss can be incorporated in the standard Child-Langmuir framework by introducing an effective potential. The modified Child-Langmuir law can be used to predict the maximum power loss for a given plate separation and potential difference as well as the maximum transmitted current for this power loss. The effectiveness of the theory is tested numerically.

physics.plasm-ph↗

arXiv2004

Generalization of Child-Langmuir Law for Non-Zero Injection Velocities in a Planar Diode

The Child-Langmuir law relates the voltage applied across a planar diode to the saturation value J_CL of current density that can be transmitted through it in case the injection velocity of electrons into the diode is zero. The Child-Langmuir current density J_CL is, at the same time, (i) the maximum current density that can be transmitted through a planar diode, (ii) the current density below which the flow is steady and unidirectional in the long time limit and (iii) the average transmitted current density for {\em any} value of injected current density above J_CL. Existing generalizations of Child-Langmuir law to non-zero velocities of injection are based on the characteristics (i) and (ii) of J_CL. This paper generalizes the law to non-zero velocities of injection based on the characteristic (iii) by deriving an analytical expression for the saturation value of current density. The analytical expression for the saturation current density is found to be well supported by numerical computations. A reason behind preferring the saturation property of the Child-Langmuir current density as the basis for its generalization is the importance of that property in numerical simulations of high current diode devices.

physics.plasm-ph↗

arXiv2004

Classical projected phase space density of billiards and its relation to the quantum Neumann spectrum

A comparison of classical and quantum evolution usually involves a quasi-probability distribution as a quantum analogue of the classical phase space distribution. In an alternate approach that we adopt here, the classical density is projected on to the configuration space. We show that for billiards, the eigenfunctions of the coarse-grained projected classical evolution operator are identical to a first approximation to the quantum Neumann eigenfunctions. However, even though there exists a correspondence between the respective eigenvalues, their time evolutions differ. This is demonstrated numerically for the stadium and lemon shaped billiards.

nlin.CD↗

arXiv2004

Absence of saturation for finite injected currents in axially symmetric cavity diode

The Child-Langmuir law is investigated numerically using a fully electromagnetic particle-in-cell code for a closed axially symmetric diode. It is found that the average current transmitted to the anode increases with the injected current even after the formation of virtual cathode in both the non-relativistic and relativistic cases. The increase is found to be a power law. In other words, the time averaged fraction $f$ of electrons reaching the anode varies with the input current as, $f\sim J_{\rm IN}^{-β}$ where $β< 1$. In contrast, for an infinite parallel plate diode, $f \sim J_{\rm IN}^{-1}$. The possibility of asymptotic saturation is also discussed.

physics.plasm-ph↗

arXiv2001

Measuring billiard eigenfunctions with arbitrary trajectories

We propose a method of measuring approximate quantum eigenfunctions in polygonalized billiard geometries, based on a quasiclassical evolution operator having a (smoothened) Perron-Frobenius kernel modulated by a phase arising from quantum considerations. We show that quasiclassical evolution differs from semiclassical (or quantum) evolution but the operators have the same set of eigenfunctions. We demonstrate this by determining the quasiclassical eigenfunctions of the polygonalized stadium billiard using arbitrary trajectories and comparing this with the exact quantum stadium eigenfunctions.

nlin.CD↗

arXiv2001

Semiclassical Inequivalence of Polygonalized Billiards

Polygonalization of any smooth billiard boundary can be carried out in several ways. We show here that the semiclassical description depends on the polygonalization process and the results can be inequivalent. We also establish that generalized tangent-polygons are closest to the corresponding smooth billiard and for de Broglie wavelengths larger than the average length of the edges, the two are semiclassically equivalent.

nlin.CD↗

arXiv2001

The Arbitrary Trajectory Quantization Method

The arbitrary trajectory quantization method (ATQM) is a time dependent approach to quasiclassical quantization based on the approximate dual relationship that exists between the quantum energy spectra and classical periodic orbits. It has recently been shown however, that, for polygonal billiards, the periodicity criterion must be relaxed to include closed almost-periodic (CAP) orbit families in this relationship. In light of this result, we reinvestigate the ATQM and show that at finite energies, a smoothened quasiclassical kernel corresponds to the modified formula that includes CAP families while the delta function kernel corresponding to the periodic orbit formula is recovered at high energies. Several clarifications are also provided.

nlin.CD↗

arXiv2000

Escape from noisy intermittent repellers

Intermittent or marginally-stable repellers are commonly associated with a power law decay in the survival fraction. We show here that the presence of weak additive noise alters the spectrum of the Perron - Frobenius operator significantly giving rise to exponential decays even in systems that are otherwise regular. Implications for ballistic transport in marginally stable miscrostructures are briefly discussed.

nlin.CD↗

arXiv2000

Closed almost-periodic orbits in semiclassical quantization of generic polygons

Periodic orbits are the central ingredients of modern semiclassical theories and corrections to these are generally non-classical in origin. We show here that for the class of generic polygonal billiards, the corrections are predominantly classical in origin owing to the contributions from closed almost-periodic (CAP) orbit families. Furthermore, CAP orbit families outnumber periodic families but have comparable weights. They are hence indispensable for semiclassical quantization.

chao-dyn↗

arXiv1999

Distribution of Husimi Zeroes in Polygonal Billiards

The zeroes of the Husimi function provide a minimal description of individual quantum eigenstates and their distribution is of considerable interest. We provide here a numerical study for pseudo- integrable billiards which suggests that the zeroes tend to diffuse over phase space in a manner reminiscent of chaotic systems but nevertheless contain a subtle signature of pseudo-integrability. We also find that the zeroes depend sensitively on the position and momentum uncertainties with the classical correspondence best when the position and momentum uncertainties are equal. Finally, short range correlations seem to be well described by the Ginibre ensemble of complex matrices.

chao-dyn↗

arXiv1998

Quantizing Billiards with Arbitrary Trajectories

The structure of the semiclassical trace formula can be used to construct a quasi-classical evolution operator whose spectrum has a one-to-one correspondence with the semiclassical quantum spectrum. We illustrate this for marginally unstable integrable and non-integrable billiards and demonstrate its utility by quantizing them using arbitrary non-periodic trajectories.

chao-dyn↗

arXiv1998

Effect of Boundary Conditions on Fluctuations Measures

A change in boundary conditions (BC) from uniform Dirichlet to non-identical BC on the edges of a triangular billiard often brings about a dramatic change in quantum spectral fluctuations. We provide a theory for this based on periodic orbits and show that non-identical BC on adjacent edges can lead to a quantum splitting of periodic orbit families which results in a significant change in the form factor. Thus, the classical spectrum alone cannot determine quantum correlations.

chao-dyn↗

arXiv1997

Symmetry Reduction and Semiclassical Analysis of Axially Symmetric Systems

We derive a semiclassical trace formula for a symmetry reduced part of the spectrum in axially symmetric systems. The classical orbits that contribute are closed in (ρ,z,p_ρ,p_z) and have p_ϕ= m\hbar where m is the azimuthal quantum number. For m > 0, these orbits vary with energy and almost never lie on periodic trajectories in the full phase space in contrast to the case of discrete symmetries. The transition from m=0 to m > 0 is however not dramatic as our numerical results indicate, suggesting that contributing orbits occur in topologically equivalent families within which p_ϕvaries smoothly.

chao-dyn↗