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Siddhant Das

Publications and source records attributed to Siddhant Das.

18 recordsLinked to original sources
arXiv2026

Exact propagating Dirac wave packets in an attractive Coulomb-like potential

We construct exact, positive-energy, normalizable wave-packet solutions of the Dirac equation in the axisymmetric potential $V=-\,v_0/\rho$ -- to our knowledge, the first such solutions in any external potential. Remarkably, one family comprises only elementary functions whose longitudinal profiles reproduce the free-Schr\"odinger Hermite--Gauss wave packets in the nonrelativistic limit. All packets share two striking features: (i) a probability density that is pointwise decoupled from spin orientation -- despite the inherent spin-orbit coupling of the Dirac equation -- and (ii) a complete freezing of their time evolution at the critical coupling $v_0\to\hbar c/2$. We also present a simple scheme that maps solutions of the 2D Helmholtz equation to further exact Dirac wave packets.

quant-ph↗
arXiv2025

Absorbing detectors meet scattering theory

Any proposed solution to the "screen problem" in quantum mechanics -- the challenge of predicting the joint distribution of particle arrival times and impact positions -- must align with the extensive data obtained from scattering experiments. In this paper, we conduct a direct consistency check of the Absorbing Boundary Condition (ABC) proposal, a prominent approach to address the screen problem, against the predictions derived from scattering theory (ST). Through a series of exactly solvable one- and two-dimensional examples, we demonstrate that the ABC proposal's predictions are in tension with the well-established results of ST. Specifically, it predicts sharp momentum- and screen-orientation-dependent detection probabilities, along with secondary reflections that contradict existing experimental data. We conclude that while it remains possible that physical detectors described by the ABC proposal could be found in the future, the proposal is empirically inadequate as a general solution to the screen problem, as it is inconsistent with the behavior of detectors in standard experimental settings.

quant-ph↗
arXiv2024

Spin-aware movement of electrons and time-of-flight momentum spectroscopy

In the framework of the de Broglie-Bohm pilot-wave theory, or Bohmian mechanics, we examine two pedagogical problems that illustrate the bound and unbound motion of spin-1/2 particles: First, a single spin-1/2 particle trapped in the ground state of a spherical box is studied in both the relativistic and nonrelativistic versions of the theory; second, the free time evolution of this particle once the confinement is released is examined, demonstrating how the Fourier transform of the prepared wave function yields the statistics of the particle's far-field (asymptotic) velocity, thereby providing a deeper understanding of time-of-flight momentum spectroscopy techniques.

quant-ph↗
arXiv2023

Detlef Dürr, arrival-time distributions, and spin in Bohmian mechanics: Personal recollections and state-of-the-art

I recount here my association with Prof. Detlef Dürr leading to our memorable research collaboration on arrival-time distributions in quantum mechanics. He influenced my life, both personally and professionally, as few others have or ever will. Detlef is my role model for what a brilliant, discerning scientist, academic, and mentor can and should be. The "arrival-time problem" in quantum mechanics is examined selectively, with an emphasis on the arrival-time distributions of Bohmian particles. In what follows, the "exotic" Bohmian arrival-time distributions of spin-polarized electrons accelerating down a cylindrical waveguide [S. Das and D. Dürr, Sci. Rep. 9: 2242 (2019)], and some variations thereof are discussed. I shall not go into the mathematical treatment more than is necessary to spell out the key results. The intention is to document the circumstances and motivations underlying the ideas.

physics.hist-ph↗
arXiv2022

Double-slit experiment revisited

The double-slit experiment is one of the quintessential quantum experiments. However, it tends to be overlooked that a theoretical account of this experiment requires the specification of the joint position and time distribution of detection at the screen, whose position marginal yields the famous interference pattern. The difficulty then arises what this distribution should be. While there exists a variety of proposals for a quantum mechanical time observable, there is no consensus about the right choice. Here, we consider Bohmian mechanics, which allows for a natural and practical approach to this problem. We simulate this distribution in the case of an initial Gaussian wave packet passing through a double-slit potential. We also consider a more challenging setup in which one of the slits is shut during flight. To experimentally probe the quantum nature of the time distribution, a sufficient longitudinal spread of the initial wave packet is required, which has not been achieved so far. Without sufficient spread, the temporal aspect of the distribution can be treated classically. We illustrate this for the case of the double-slit experiment with helium atoms by Kurtsiefer et al. [Nature 386, 150 (1997)], which reports the joint position and time distribution.

quant-ph↗
arXiv2021

Relativistic electron wave packets featuring persistent quantum backflow

Closed-form, normalizable solutions of Dirac's equation propagating within a semi-infinite cylindrical waveguide are obtained in terms of ordinary and modified Bessel functions. These relativistic wave packets induce quantum backflow on a cross-section of the cylinder at practically any distance along the waveguide, becoming spin-polarized in the nonrelativistic limit. The predicted backflow is stable in time and is manifest regardless of the initial wave function.

quant-ph↗
arXiv2021

Questioning the adequacy of certain quantum arrival-time distributions

It is shown that a class of exponentially decaying time-of-arrival probability distributions suggested by Włodarz, Marchewka and Schuss, and Jurman and Nikolić, as well as a semiclassical distribution implicit in time-of-flight momentum measurements, do not show the expected behavior for a Gaussian wave train. This casts doubts on the physical adequacy of these arrival-time proposals. In contrast, the quantum flux distribution (a special case of the Bohmian arrival-time distribution) displays the expected behavior.

quant-ph↗
arXiv2021

Times of Arrival and Gauge Invariance

We revisit the arguments underlying two well-known arrival-time distributions in quantum mechanics, viz., the Aharonov-Bohm and Kijowski (ABK) distribution, applicable for freely moving particles, and the quantum flux (QF) distribution. An inconsistency in the original axiomatic derivation of Kijowski's result is pointed out, along with an inescapable consequence of the "negative arrival times" inherent to this proposal (and generalizations thereof). The ABK free-particle restriction is lifted in a discussion of an explicit arrival-time setup featuring a charged particle moving in a constant magnetic field. A natural generalization of the ABK distribution is in this case shown to be critically gauge-dependent. A direct comparison to the QF distribution, which does not exhibit this flaw, is drawn (its acknowledged drawback concerning the quantum backflow effect notwithstanding).

quant-ph↗
arXiv2019

Exotic Bohmian arrival times of spin-1/2 particles I-An analytical treatment

It is well known that orthodox quantum mechanics does not make unambiguous predictions for the statistics in arrival time (or time-of-flight) experiments. Bohmian mechanics (or de Broglie-Bohm theory) offers a distinct conceptual advantage in this regard, owing to the well defined concepts of point particles and trajectories embedded in this theory. We revisit a recently proposed experiment [S. Das and D. Dürr, Sci. Rep. (2019)], the numerical analysis of which revealed a striking spin dependence in the (Bohmian) time-of-arrival distributions of a spin-1/2 particle. We present here a mathematically tractable variant of the same experiment, where the predicted effects can be established rigorously. We also obtain some new results that can be compared with experiment.

quant-ph↗
arXiv2018

Arrival Time Distributions of Spin-1/2 Particles

The arrival time statistics of spin-1/2 particles governed by Pauli's equation, and defined by their Bohmian trajectories, show unexpected and very well articulated features. Comparison with other proposed statistics of arrival times that arise from either the usual (convective) quantum flux or from semiclassical considerations suggest testing the notable deviations in an arrival time experiment, thereby probing the predictive power of Bohmian trajectories. The suggested experiment, including the preparation of the wave functions, could be done with present-day experimental technology.

quant-ph↗
arXiv2018

Quantum First Passage Time Problem-A Bohmian Perspective

The prediction of arrival time or first passage time statistics of a quantum particle is an open problem, which challenges the foundations of quantum theory. One of the most promising and insightful approaches to this problem stems from the de Broglie-Bohm pilot-wave theory (a.k.a Bohmian mechanics). Applying the fundamental postulates of this theory, we analyze a simplified first passage time experiment and derive the empirical passage time distribution $\Pi(\tau)$. Implications of our results are also discussed.

quant-ph↗
arXiv2016

Exact energy quantization condition for single Dirac particle in one-dimensional (scalar) potential well

We present an exact quantization condition for the time independent solutions (energy eigenstates) of the one-dimensional Dirac equation with a scalar potential well that gives only two `effective' turning points (defined by the roots of $V(x)+mc^2=\pm E$) for a given energy $E$ and satisfies $\min V(x)+mc^2\geq 0$. This result generalizes the previously known non-relativistic quantization formula and preserves many physically desirable symmetries, besides, attaining the correct non-relativistic limit. Numerical calculations demonstrate the utility of the formula for computing accurate energy eigenvalues.

quant-ph↗
arXiv2015

Bound states of a two-dimensional electron gas in inhomogeneous magnetic fields

We study the bound states of a two dimensional free electron gas (2DEG) subjected to a perpendicular inhomogeneous magnetic field. An analytical transfer matrix (ATM) based exact quantization formula is derived for magnetic fields that vary (arbitrarily) along one spatial direction. As illustrative examples, we consider (1) a class of symmetric power law magnetic fields confined within a strip, followed by the problem of a (2) 2DEG placed under a thin ferromagnetic film, which are hitherto unexplored. The exact Landau levels for either cases are obtained. Also, the role of the fringing magnetic field (present in the second example) on these levels is discussed.

cond-mat.mes-hall↗
arXiv2014

Tunneling Through a One-Dimensional Piece Wise Constant Potential Barrier

In this paper we look at transmission through one-dimensional potential barriers that are piece wise constant. The Transfer Matrix approach is adopted and a new formula is derived for multiplying long matrix sequences that not only leads to an elegant representation of the wave function, but also results in much faster computation than earlier methods. The proposed method covers a broad spectrum of potentials of which multi-barrier systems are special cases. The paradigm is exemplified with a finite lattice of non-uniform rectangular barriers - non-uniformity being crucial, as the uniform case has been solved exactly by Griffiths and Steinke. For the non-uniform multi-barrier problem, the intervening wells strongly influence the transmission probability. Surprisingly, we find that the wells act 'individually', i.e. their influence is only a function of their width and is independent of their exact 'location' in a multi-barrier system. This leads to a startling observation, which we have termed as the 'Alias Effect.' The exact solutions are supported with asymptotic formulas.

quant-ph↗
arXiv2013

Exact Solution for One Dimensional Multibarrier Tunneling

Quantum tunneling across multiple barriers as yet is an unsolved problem for barrier numbers greater than five. The complexity of the mathematical analysis even for small number of barriers pushed it into the realms of Numerical Analysis. This work is aimed at providing a rigorously correct solution to the general N barrier problem, where N can be any positive integer. An exact algebraic solution has been presented, which overcomes the complexity of the WKB integrals that are traditionally employed, and matches the earlier results reported for small number of barriers. The solution has been explored to considerable depth and many startling consequences have been pointed out for 500 and 1000 barriers. These are quite revealing and open up many avenues for engineering applications and further research.

quant-ph↗