arXiv subjects

Avi Marchewka

Publications and source records attributed to Avi Marchewka.

At least 19 recordsLinked to original sources

arXiv2026

Deriving the Kijowski Arrival-Time POVM from the Schr\"odinger Current: Minimal Positivity and Uniqueness

Quantum backflow refers here to the appearance of a negative Schr\"odinger current for a state whose momentum support is entirely positive. We ask for the smallest modification of the free Schr\"odinger current that makes it nonnegative for every such state, while preserving the current of each individual momentum component. We show that the required minimal modification changes the free-particle momentum kernel according to \[ K_{\rm Sch}(p,p')=\frac{p+p'}{2m} \;\longrightarrow\; K_{\min}(p,p')=\frac{\sqrt{pp'}}{m}. \] The resulting current is positive and normalized and therefore defines an arrival-time POVM. Extending the directional no-backflow requirement to states containing both momentum signs forces the cross-sector kernel to vanish, \[ K_{\min}^{+-}=K_{\min}^{-+}=0, \] so that the full current is the sum of two independent directional contributions. The resulting POVM is exactly the Kijowski time-of-arrival POVM, providing a current-based physical motivation for both its directional kernels and their separation. Within the diagonal-preserving pairwise-minimal construction considered here, the result is unique. The construction itself does not impose a first-arrival condition.

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arXiv2026

The MS Unidirectional Current as a Generalization of the ABC Absorption Current

For a free scalar particle in one spatial dimension, in a single-pass half-line geometry, we compare the absorbing Robin boundary condition with the generalized Marchewka--Schuss (MS) unidirectional-current family. Robin absorption is characterized by a single parameter $\kappa>0$: once $\kappa$ is specified, its momentum-dependent absorption profile is fixed. In the generalized MS construction, by contrast, the detector response is described by a spectral function $\lambda(k)$, subject to the positivity and subnormalization conditions of the detection law. We show that every Robin choice of $\kappa$ corresponds to the particular MS calibration $\lambda_\kappa(k)=\pi\kappa/(k+\kappa)^2$, which reproduces the complete Robin absorption current for every admissible one-sided spectral amplitude and at every time. Thus the entire one-parameter Robin absorption family is contained within the generalized MS family. The MS construction is more general: the choice $\lambda_{\rm full}(k)=\pi/(4k)$ gives unit absorption efficiency for every wave number, which cannot be achieved by any fixed Robin parameter. In this precise sense, the generalized MS detector process extends the Robin absorbing-boundary family. We also compare their asymptotic behavior in the ballistic fixed-ray regime and in the fixed-distance late-time limit.

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arXiv2026

The Unidirectional Current as First Arrival-Time POVM: An MS-Kijowski Identity, Physical Interpretation, and Mathematical Applications

Detector-based first-arrival models and operator-based arrival-time observables provide two conceptually distinct approaches to the quantum time-of-arrival problem. Here we connect these approaches by using the positive unidirectional first-arrival current of Marchewka and Schuss (MS) as the basis for constructing a family of positive arrival-time operators and, after normalization, an arrival-time POVM. The first-arrival character is inherited from the dynamics with a Dirichlet boundary, while the detector response is introduced at the amplitude level through a non-negative spectral function $\lambda(k)$. For a one-dimensional free particle, resolution of the identity uniquely selects $\lambda(k)=\frac{\pi}{4k}$, yielding an arrival-time POVM. The normalized unidirectional current can therefore be interpreted as a generalized Born-rule probability density rather than as a hazard rate, as in the original MS formulation. We further show that the normalized one-sided MS amplitude coincides, up to an irrelevant phase, with the corresponding momentum-sector amplitude in Kijowski's arrival-time distribution. Consequently, the two directional contributions in Kijowski's distribution can be reproduced by two first-arrival problems defined on opposite sides of the boundary. This establishes an equivalence between the resulting arrival-time statistics while emphasizing the different physical interpretations: MS describes a first-arrival process with coherent momentum components, whereas Kijowski's POVM treats the two momentum sectors as separate directional contributions. Thus, the normalized unidirectional current provides a POVM description of first arrival at a point, combining detector-based dynamics with a positive-operator measurement structure.

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arXiv2024

The Paradox of the Recoil Force Acting on a Leaking Water Tank

In the first part of the article, we will outline the paradoxical picture that arises when attempting to calculate the recoil force of the water leakage from a hole at the bottom of a water tank. We will present three different options for the recoil force acting on the water tank as a result of this leakage (in Chapters 1, 2 and 3). In the second part of the article, we will present an experiment that resolves this question (in Chapter 4). Finally (in Chapter 5), we will present a coherent picture of the description of the leakage and the result recoil force.

physics.class-ph↗

arXiv2022

A direct test for instantaneous collapse of wave functions in configuration space

Wavefunction collapse is a puzzling aspect of quantum mechanics. Designing a test to confirm the instantaneousness of collapse has turned out to be challenging, especially for collapse in configuration space. We propose a test using two identical, non-local, correlated photons in an interferometer in which a post-selection measurement of one of the photons in its location changes the statistical behavior of the other photon, which is an arbitrarily large distance away, and thus its detectable subsequent behavior. Analysis of the resulting correlations constitutes a test of the instantaneousness (or non-instantaneousness) of collapse. Connections to some of the recent proposed models of collapse are discussed

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arXiv2021

Full Realization Scheme of the Tensor Product Space of N Distinguishable Photons in Two States

The ability to control and hence to realize a given number of photons is of major interest from a fundamental point of view, e.g. Bell inequalities, photons bunching. In recent years this interest has grown by the so-called the "Second Quantum Revolution" where such an ability is needed for quantum computers, etc. In this paper, we show that such a realization can not be done by a unitary process. Therefore, a non-unitary interferometer is given to build a full realization of the tensor product space for two photons at two states. Finally, by modifying the previous interferometer, the full tonsorial product space of N photons in two states is shown.

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arXiv2020

A bunching parameter interferometer: Generalization of HOM effect

Are photons either bunched or unbunched, or are these particular cases of a wider phenomenon? Here we will show that bunched and unbunched photons are indeed two extreme cases of a process parameterized by a continuous parameter, called the bunching parameter, and (mainly) we will suggest a bunching interferometer that can be used for the construction and measurement of the full range of values of the above bunching parameter. Finally, as an application of the bunching parameter, we will show how the dip graph of the HOM effect is generalized

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arXiv2020

Coefficient of restitution: Derivation of Newtonś Experimental Law from general energy considerations

In order to describe the velocity of two bodies after they collide, Newton developed a phenomenological equation known as "Newton\' s Experimental Law" (NEL). In this way, he was able to practically bypass the complication involving the details of the force that occurs during the collision of the two bodies. Today, we use NEL together with momentum conservation to predict each bodyś velocity after collision. This, indeed, avoids the complication of knowing the forces involved in the collision, making NEL very useful. Whereas in Newtonś days the quantity of kinetic energy was not known, today it is a basic quantity that is in use. In this paper we will use the loss (or gain) of kinetic energy in a collision to show how NEL can be derived.

physics.class-ph↗

arXiv2017

The case of escape probability as linear in short time

We derive rigorously the short-time escape probability of a quantum particle from its compactly supported initial state, which has a discontinuous derivative at the boundary of the support. We show that this probability is liner in time, which seems to be a new result. The novelty of our calculation is the inclusion of the boundary layer of the propagated wave function formed outside the initial support. This result has applications to the decay law of the particle, to the Zeno behavior, quantum absorption, time of arrival, quantum measurements, and more, as will be discussed separately.

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arXiv2016

State Orthogonality, Boson Bunching Parameter and Bosonic Enhancement Factor

It is emphasized that the bunching parameter $β=P_B/P_D$ , i.e. the ratio between the probability to measure two bosons and two distinguishable particles at the same state, is a constant of motion and depends only on the overlap between the initial wavefunctions. This ratio is equal to $β=2/(1+I^2)$ , where $I$ is the overlap integral between the initial wavefunctions. That is, only when the initial wavefunctions are orthogonal this ratio is equal to 2, however, this bunching ratio can be reduced to 1, when the two wavefunctions are identical. This simple equation explains the experimental evidences of a beam splitter. A straightforward conclusion is that by measuring the local bunching parameter $β$ (at any point in space and time) it is possible to evaluate a global parameter$ I$ (the overlap between the initial wavefunctions). The bunching parameter is then generalized to arbitrary number of particles, and in an analogy to the two-particles scenario, the well-known bosonic enhancement appears only when all states are orthogonal.

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arXiv2016

On the spatial coordinate measurement of two identical particles

Theoretically, the coordinate measurement of two identical particles at a point by two narrowly separated narrow detectors, is interpreted in the limit of shrinking width and separation, as the detection of two particles by a single narrow detector. { Ordinarily, the ratio between probabilities of point measurements is independent of the width of the narrow detectors.} We show here that not only this is not the case, but that in some scenarios the results depend on the way the dimensions shrink to zero. The ratio between the width and the separation determines the detection result. { In particular, it is shown that the bunching parameter of bosons is not a well-defined physical property. Moreover, it may suggests that } there is a difficulty in quantum measurement theory in the interpretation of coordinate measurement of two particles.

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arXiv2013

Zeros in Bosonic Wave-Function Result in Local Anti-Bunching: Refining Feynman's argument

The effect of boson bunching is frequently mentioned and discussed in the literature. This effect is the manifestation of bosons tendency to "travel" in clusters. One of the core arguments for boson bunching was formulated by Feynman in his well-known lecture series and has been frequently used ever since. By comparing the scattering probabilities of two bosons and of two non-identical particles, Feynman concluded: "We have the result that it is twice as likely to find two identical Bose particles scattered into the same state as you would calculate assuming the particles were different." [1]. Indeed, in most scenarios, this reasoning is valid, however, as it is shown in this paper, there are cases, even in the most ordinary scattering scenarios, where this reasoning is invalid, and in fact the opposite occurs: boson anti-bunching appears. Similarly, it is shown that at exactly the same scenarios, fermions bunch together.

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arXiv2013

Quantum Dynamics Arising from Statistical Axioms

We investigate the dynamics of pairs of Fermions and Bosons released from a box and find that their populations have unique generic properties ensuing from the axioms of quantum statistics and symmetries. These depend neither on the specific equations of wave function propagation, such as Schrödinger, Klein-Gordon, Dirac, nor on the specific potential involved. One surprising finding is that after releasing the pairs, there are always more Boson than Fermion pairs outside the box. Moreover, if the initial wave functions have the same symmetry (odd or even), then there is a higher chance for a Boson than a Fermion pair to escape from the trap in opposite directions, as if they repel each other. We calculate the wave functions exactly, numerically, and asymptotically for short time and demonstrate these generic results in the specific case of particles released from an infinite well.

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arXiv2010

Bound Eigenstate dynamics under a sudden shift of the well's wall

We investigate the dynamics of the eigenstate of an infinite well under an abrupt shift of the well's wall. It is shown that when the shift is small compared to the initial well's dimensions, the short time behavior changes from the well known t^(3/2) behavior to t^(1/2) . It is also shown that the complete dynamical picture converges to a universal function, which has fractal structure with dimensionality D=1.25.

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arXiv2010

Transients with time-independent currents

It is shown that when the initial particles probability density is discontinuous the emerging currents appear instantaneously, and although the density beyond the discontinuity is initially negligible the currents there have a finite value. It is shown that this non-equilibrium effect can be measured in real experiments (such as cooled Rubidium atoms), where the discontinuity is replaced with finite width (hundreds of nanometers) gradient.

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arXiv2010

Trapping of quantum particles and light beams by switchable potential wells

We consider basic dynamical effects in settings based on a pair of local potential traps that may be effectively switched on and off, or suddenly displaced, by means of appropriate control mechanisms, such as the scanning tunneling microscopy (STM) or photo-switchable quantum dots. The same models, based on the linear Schrodinger equation with time-dependent trapping potentials, apply to the description of optical planar systems designed for the switching of trapped light beams. The analysis is carried out in the analytical form, using exact solutions of the Schrodinger equation. The first dynamical problem considered in this work is the retention of a particle released from a trap which was suddenly turned off, while another local trap was switched on at a distance - immediately or with a delay. In this case, we demonstrate that the maximum of the retention rate is achieved at a specific finite value of the strength of the new trap, and at a finite value of the temporal delay, depending on the distance between the two traps. Another ptoblem is retrapping of the bound particle when the addition of the second trap transforms the single-well setting into a double-well potential (DWP). In that case, we find probabilities for the retrapping into the ground or first excited state of the DWP. We also analyze effects entailed by the application of a kick to a bound particle, the most interesting one being a kick-induced transition between the DWP's ground and excited states. In the latter case, the largest transition probability is achieved at particular strength of the kick.

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arXiv2008

Quantum particle displacement by a moving localized potential trap

We describe the dynamics of a bound state of an attractive $δ$-well under displacement of the potential. Exact analytical results are presented for the suddenly moved potential. Since this is a quantum system, only a fraction of the initially confined wavefunction remains confined to the moving potential. However, it is shown that besides the probability to remain confined to the moving barrier and the probability to remain in the initial position, there is also a certain probability for the particle to move at double speed. A quasi-classical interpretation for this effect is suggested. The temporal and spectral dynamics of each one of the scenarios is investigated.

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arXiv2008

A quantum decay model with exact explicit analytical solution

A simple decay model is introduced. The model comprises of a point potential well, which experiences an abrupt change. Due to the temporal variation the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a \textit{fractional} power law, which differs from perturbation quantum methods predictions.

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