arXiv subjects

P. Singha Deo

Publications and source records attributed to P. Singha Deo.

At least 19 recordsLinked to original sources

arXiv2026

Reinterpreting Landauer conductance, solving the quantum measurement problem, grand unification

In a series of recent papers we have proved rigorously that time travel is a reality and very much feasible by using quantum mechanical processes. There are plenty of indirect experimental support untill a direct experiment is conducted. The process crucially depend on the reality of a local time as well as a local partial density of states (LPDOS) that can become negative very easily in the quantum regime of mesoscopic systems. Mesoscopic systems are small enough to allow us to experimentally access the intermediate regime between the classical and quantum worlds. This LPDOS is in every sense a hidden variable in quantum mechanics that does not show up in the axiomatic framework of quantum mechanics. It can be inferred through physical clocks obeying quantum dynamics and can be rigorously justified from the properties of the Hilbert space that is uniquely isomorphic to the complex plane. Therefore one can naturally guess that LPDOS will have something important to say about quantum measurement as well as the unification of classical and quantum laws. We therefore undertake the exercise to show that LPDOS can very much allow us to re-interpret the enormously successful phenomenological Landauer-Buttiker formalism for mesoscopic systems and put it on firm theoretical ground as a bridge between classical and quantum mechanics, thereby unifying them. Essentially the local time calculated quantum mechanically can dilate exactly like the proper time of relativity and be consistent with the coordinate time of relativity. Also the measured conductance of mesoscopic samples is a deterministic quantum measurement outcome from a linear superposition of states, essentially because of LPDOS, which solves the quantum measurement problem. For this we analyze the three probe conductance formula in details and give our arguments for the general case.

cond-mat.mes-hall↗

arXiv2025

Negative Local Partial Density of States

Real quantum systems can exhibit a local object called local partial density of states (LPDOS) that cannot be proved within the axiomatic approach of quantum mechanics. We demonstrate that real mesoscopic system that can exhibit Fano resonances will show this object and also very counterintuitively it can become negative, resulting in the enhancement of coherent currents.

quant-ph↗

arXiv2025

Multiple Manifestations of Negative Local Partial Density of States

We revealed that with the measurement of the scattering phase shift of electron in low-dimensional or mesoscopic systems local objects of hierarchy of density of states can also determine experimentally. In recent times, it has been exhibited that in mesoscopic systems certain objects of density of states (DOS) hierarchy like local partial DOS, partial DOS, injectivity, emissivity, etc. can become negative in presence of Fano resonance. Negativity of local partial density of states can be interpreted as the losing coherent electrons in reverse time. This may have implications for the thermodynamic properties of these mesoscopic systems. In these negative local partial states, electrons may behave akin to positrons, resulting in practical the possibility of electron-electron interaction. The objective of this research is to reveal some manifestations of local objects in mesoscopic systems, employing rigorous calculations utilizing two different approaches: a continuum model and a discrete or tight binding model. It has been demonstrated that negative local partial states are correlated with Fano-resonance featuring a π phase drop.

cond-mat.mes-hall↗

arXiv2022

Time Reversed States in Barrier Tunneling

Tunneling, though a physical reality, is shrouded in mystery. Wave packets cannot be constructed under the barrier and group velocity cannot be defined. The tunneling particle can be observed on either sides of the barrier but its properties under the barrier has never been probed due to several problems related to quantum measurement. We show that there are ways to bypass these problems in mesoscopic systems and one can even derive an expression for the quantum mechanical current under the barrier. A general scheme is developed to derive this expression for any arbitrary system. One can use mesoscopic phenomenon to subject the expression to several theoretical and experimental cross checks. For demonstration we consider an ideal 1D quantum ring with Aharonov-Bohm flux $Φ$, connected to a reservoir. It gives clear evidence that propagation occur under the barrier resulting in a current that can be measured non-invasively and theoretically cross checked. Time reversed states play a role but there is no evidence of violation of causality. The evanescent states are known to be largely stable and robust against phase fluctuations making them a possible candidate for device applications and so formalizing current under barrier is important.

cond-mat.mes-hall↗

arXiv2022

A Mechanism to Attract Electrons

In a startling discovery it has been recently found that certain density of states (DOS) can become negative in mesoscopic systems wherein electrons can travel back in time. We give a brief introduction to the hierarchy of density of states in mesoscopic systems as we want to point out some robust phenomenon that can be experimentally observed with our present day technologies. They can have direct consequences on thermodynamic effects and also can provide indirect evidence of time travel. Essentially certain members of the hierarchy of DOS become negative in these regimes and that can attract other electrons.

cond-mat.mes-hall↗

arXiv2018

Transmitting a signal in negative time

There is no self adjoint time operator defined in quantum mechanics. However, time intervals can be defined in several ways and can also be probed experimentally. Our interest in this work is traversal time and signal propagation time. According to Copenhagen interpretation of quantum mechanics the two should be the same but the issue is not settled yet in regimes where they can be negative. We use Argand diagram and Burgers circuit to show that the correct traversal time and the correct signal propagation time can be identically negative implying signal can be propagated in negative time. Some other physical consequences are discussed.

quant-ph↗

arXiv2017

A Study of Topological Quantum Phase Transition and Majorana Localization Length for the Interacting Helical Liquid System

We consider a helical spin liquid system which shows majorana fermion modes at the edge. The interaction between the quasiparticles in this system induces phase transition, Majorana-Ising transition. We comply the density matrix renormalization group method to study this phase transition for the entire regime of the parameter space. We observe the presence of topological quantum phase transition for repulsive interaction, however this phase is more stable for the attractive interaction. The length scale dependent study shows many new and important results and we show explicitly that the major contribution to the excitation comes from the edge of the system when the system is in the topological state. We also show the dependence of Majorana localization length for various values of chemical potential.

cond-mat.str-el↗

arXiv2016

Negative partial density of states in mesoscopic systems

Since the experimental observation of quantum mechanical scattering phase shift in mesoscopic systems, several aspects of it has not yet been understood. The experimental observations has also accentuated many theoretical problems related to Friedel sum rule and negativity of partial density of states. We address these problems using the concepts of Argand diagram and Burgers circuit. We can prove the possibility of negative partial density of states in mesoscopic systems. Such a conclusive and general evidence cannot be given in one, two or three dimensions. We can show a general connection between phase drops and exactness of semi classical Friedel sum rule. We also show Argand diagram for a scattering matrix element can be of few classes based on their topology and all observations can be classified accordingly.

cond-mat.mes-hall↗

arXiv2014

Current carried by evanescent modes and possible device application

Quantum tunneling of an electron through a classically forbidden regime has no classical analogue and several aspects of it are still not well understood. In this work we analyze electronic currents under the barrier. For this we consider a multichannel Aharonov-Bohm ring and developed a correct formalism to calculate the currents inside the ring when the states are evanescent. We also show unlike other proposed quantum devices that such currents and associated conductance are not very sensitive to changes in material parameters and thus the system can be used to build stable devices that work on magnetic and transport properties. We also study the current magnification property of the ring in presence of both propagating and evanescent states.

cond-mat.mes-hall↗

arXiv2013

Charge and spin density waves: Quasi one dimension to two dimension

Possibility of electronic charge and spin separation leading to charge density wave and spin density wave is well established in one dimensional systems in presence and absence of Coulomb interaction. We start from quasi one dimension and show the possibility of such a transition in quasi one dimension as well as in two dimension by going to a regime where it can be shown for free electrons that just interact via Fermi statistics. Since Coulomb interaction can only facilitate the phenomenon, the purpose of our work is to show the phenomena unambiguously in the limit when Coulomb interaction can be ignored. Finally we also comment on dimensions greater than two and inclusion of Coulomb interactions.

cond-mat.mes-hall↗

arXiv2012

Stable switch action based on quantum interference effect

Although devices working on quantum principles can revolutionize the electronic industry, they have not been achieved yet as it is difficult to control their stability. We show that one can use evanescent modes to build stable quantum switches. The physical principles that make this possible is explained in detail. Demonstrations are given using a multichannel Aharonov - Bohm interferometer. We propose a new $S$ matrix for multichannel junctions to solve the scattering problem.

cond-mat.mes-hall↗

arXiv2011

Quantum capacitance: a microscopic derivation

We start from microscopic approach to many body physics and show the analytical steps and approximations required to arrive at the concept of quantum capacitance. These approximations are valid only in the semi-classical limit and the quantum capacitance in that case is determined by Lindhard function. The effective capacitance is the geometrical capacitance and the quantum capacitance in series, and this too is established starting from a microscopic theory.

cond-mat.mes-hall↗

arXiv2011

Injectance and a paradox

Quantum mechanics manifests in experimental observations in several ways. Hauge et al. (1987) and Leavens et al. (1989) had pointed out that interference effects dominate a physical quantity called injectance. We show that, very paradoxically, the interference related term vanish in a quantum regime making semi-classical formula for injectance exact in this regime. This can have useful implications to experimentalists as semi-classical formulas are much more simple. There are other puzzling facts in this regime like an ensemble of particles can be transmitted without any time delay or negative time delays, whereas the reflected particles are associated with a time delay.

cond-mat.mes-hall↗

arXiv2009

S-Matrix Formulation of Mesoscopic Systems and Evanescent Modes

The Landauer-Butikker formalism is an important formalism to study mesoscopic systems. Its validity for linear transport is well established theoretically as well as experimentally. Akkermans et al [Phys. Rev. Lett. {\bf 66}, 76 (1991)] had shown that the formalism can be extended to study thermodynamic properties like persistent currents. It was earlier verified for simple one dimensional systems. We study this formula very carefully and conclude that it requires reinterpretation in quasi one dimension. This is essentially because of the presence of evanescent modes in quasi one dimension.

cond-mat.mes-hall↗

arXiv2008

Non-Ergodic Mesoscopic Systems

Suppose there is a mesoscopic system connected to single channel leads. If the system is non-chaotic or non-ergodic then the thermodynamic and transport properties do not depend on impurity averaged density of states. We show that the partial density of states as well as density of states of a given system can be determined exactly from the asymptotic wave-function (or scattering matrix) at the resonances. The asymptotic wave-function can be determined experimentally without any knowledge about the quantum mechanical potential (including electron-electron interaction) or wave function in the interior of the system. Some counter intuitive relations derived here can allow this.

cond-mat.mes-hall↗

arXiv2007

Large diamagnetic persistent currents

In multichannel rings, evanescent modes will always co-exist with propagating modes. The evanescent modes can carry a very large diamagnetic persistent current that can oscillate with energy and are very sensitive to impurity scattering. This provides a natural explanation for the large diamagnetic persistent currents observed in experiments.

cond-mat.mes-hall↗

arXiv2006

Soliton like wave packets in quantum wires

At a Fano resonance in a quantum wire there is strong quantum mechanical back-scattering. When identical wave packets are incident along all possible modes of incidence, each wave packet is strongly scattered. The scattered wave packets compensate each other in such a way that the outgoing wave packets are similar to the incoming wave packets. This is as if the wave packets are not scattered and not dispersed. This typically happens for the kink-antikink solution of the Sine-Gordon model. As a result of such non-dispersive behavior, the derivation of semi-classical formulas like the Friedel sum rule and the Wigner delay time are exact at Fano resonance. For a single channel quantum wire this is true for any potential that exhibit a Fano resonance. For a multichannel quantum wire we give an easy prescription to check for a given potential, if this is true. We also show that validity of the Friedel sum rule may or may not be related to the conservation of charge. If there are evanescent modes then even when charge is conserved, Friedel sum rule may break down away from the Fano resonances.

cond-mat.mes-hall↗

arXiv2005

Charge fluctuations in coupled systems: ring coupled to a wire or ring

Coupled systems in mesoscopic regime are of interest as charge fluctuation between the sub-systems will depend on electron-electron interactions and will play a dominant role in determining their thermodynamic properties. We study some simple systems like a stub or a bubble strongly coupled to a ring. We show that for strong electron-electron interaction, there are some regimes where these charge fluctuations are quenched and charge is individually conserved in the two subsystems. This feature does not depend on choice of parameters or charge distribution.

cond-mat.mes-hall↗