Ismael Lucas Paiva

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• Doctor of Philosophy
• Senior Research Associate at University of Bristol

The interaction between a quantum charge and a dynamic source of a magnetic field is considered in the Aharonov-Bohm scenario. It is shown that, in weak interactions with a post-selection of the source, the effective vector potential is, generally, complex-valued. This leads to new experimental protocols to detect the Aharonov-Bohm phase before the...

Weak values and Kirkwood--Dirac (KD) quasiprobability distributions have been independently associated with both foundational issues in quantum theory and advantages in quantum metrology. We propose simple quantum circuits to measure weak values, KD distributions, and spectra of density matrices without the need for post-selection. This is achieved...

Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special attention. Here, we introduce and analyze a nonrelativistic framework in which each system contains an internal clo...

Complementarity plays a pivotal role in understanding a diverse range of quantum phenomena. Here, we show how the tradeoff between quantities of a complete complementarity relation is modified in an arbitrary spacetime for a particle with an internal spin. This effect stems from local Wigner rotations in the spacetime, which couple the spin to the...

The superposition of causal orders shows promise in various quantum technologies. However, the fragility of quantum systems arising from environmental interactions, leading to dissipative behavior and irreversibility, demands a deeper understanding of the possible instabilities in the coherent control of causal orders. In this work, we employ a col...

The superposition of causal order shows promise in various quantum technologies. However, the fragility of quantum systems arising from environmental interactions, leading to dissipative behavior and irreversibility, demands a deeper understanding of the possible instabilities in the coherent control of causal orders. In this work, we employ a coll...

Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special attention. Here, we introduce and analyze a nonrelativistic framework in which each system contains an internal clo...

The Aharonov–Bohm (AB) effect has been highly influential in fundamental and applied physics. Its topological nature commonly implies that an electron encircling a magnetic flux source in a field-free region must close the loop in order to generate an observable effect. In this paper, we study a variant of the AB effect that apparently challenges t...

Complementarity plays a pivotal role in understanding a diverse range of quantum phenomena. Here, we show how the tradeoff between quantities of a complete complementarity relation is modified in an arbitrary spacetime for a particle with an internal spin. This effect stems from local Wigner rotations in the spacetime, which couple the spin to the...

The Aharonov-Bohm effect is a fundamental topological phenomenon with a wide range of applications. It consists of a charge encircling a region with a magnetic flux in a superposition of wave packets having their relative phase affected by the flux. In this work we analyze this effect using an entropic measure known as realism, originally introduce...

The Aharonov-Bohm (AB) effect has been highly influential in fundamental and applied physics. Its topological nature commonly implies that an electron encircling a magnetic flux source in a field-free region must close the loop in order to generate an observable effect. In this Letter, we study a variant of the AB effect that apparently challenges...

Weak values and Kirkwood-Dirac (KD) quasiprobability distributions have been independently associated with both foundational issues in quantum theory and advantages in quantum metrology. We propose simple quantum circuits to measure weak values, KD distributions, and spectra of density matrices without the need for post-selection. This is achieved...

The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend the notion of proper time to quantum mechanics within a relational framework. Here, we use similar ideas combin...

The Aharonov-Bohm effect is a fundamental topological phenomenon with a wide range of applications. It consists of a charge encircling a region with a magnetic flux in a superposition of wavepackets having their relative phase affected by the flux. In this work, we analyze this effect using an entropic measure known as realism, originally introduce...

We formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular operators of position and momentum. In analogy with dynamical nonlocality in space associated with the modular momentum, we introduce and analyze the nonlocali...

Recently, there have been many attempts to extend the notion of proper time to quantum mechanics with the use of quantum clocks. Using a similar idea combined with the relativistic mass-energy equivalence, we consider an accelerating massive quantum particle with an internal clock system. We show that the ensuing evolution from the perspective of t...

Uncertainty relations play a crucial role in quantum mechanics. Well-defined methods exist for the derivation of such uncertainties for pairs of observables. Other approaches also allow the formulation of time-energy uncertainty relations, even though time is not an operator in standard quantum mechanics. However, in these cases, different approach...

The study of recurrences and revivals in quantum systems has attracted a great deal of interest because of its importance in the control of quantum systems and its potential use in developing new technologies. In this paper, we introduce a protocol to induce full-state revivals in a huge class of quantum walks on a d-dimensional lattice governed by...

Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how this fundamental concept and other related definitions can be applied to the study of quantum systems with the use of quantum logic...

Geometric phase is a key player in many areas of quantum science and technology. In this review article, several foundational aspects of quantum geometric phases and their relations to classical geometric phases are outlined. How the Aharonov–Bohm and Sagnac effects fit into this context is then discussed. Moreover, a concise overview of technologi...

The study of recurrences and revivals in quantum systems has attracted a great deal of interest because of its importance in the control of quantum systems and its potential use in developing new technologies. In this work, we introduce a protocol to induce full-state revivals in a huge class of quantum walks on a $d$-dimensional lattice governed b...

Geometric phase is a key player in many areas of quantum science and technology. In this review article, we outline several foundational aspects of quantum geometric phases and their relations to classical geometric phases. We then discuss how the Aharonov-Bohm and Sagnac effects fit into this context. Moreover, we present a concise overview of tec...

Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how fundamental concepts of this entropy and other related definitions can be applied to the study of quantum systems, leading to the i...

Uncertainty relations play a crucial role in quantum mechanics. Well-defined methods exist for the derivation of such uncertainties for pairs of observables. Specific methods also allow to obtain time-energy uncertainty relations. However, in these cases, different approaches are associated with different meanings and interpretations. The one of in...

We formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular operators of position and momentum. In analogy with dynamical nonlocality in space associated with the modular momentum, we introduce and analyze the nonlocali...

The interaction between a quantum charge and a quantized source of a magnetic field is considered in the Aharonov-Bohm scenario. It is shown that, if the source has a relatively small uncertainty while the particle encircles it, an effective magnetic vector potential arises and the final state of the joint system is approximately a tensor product....

We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras and describe their associated reproducing kernel spaces. The case of entire functions is of special interest, and we give a precise meaning to some power series expansions of analytic functions that appears in many algebras...

This is a dissertation in two parts. In the first one, the Aharonov-Bohm effect is investigated. It is shown that solenoids (or flux lines) can be seen as barriers for quantum charges. In particular, a charge can be trapped in a sector of a long cavity by two flux lines. Also, grids of flux lines can approximate the force associated with continuous...

It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines with an arbitrary value of magnetic flux can be used to create energetic barriers, which can be used to confine q...

We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest, and we give a precise meaning to some power series expansions of analytic functions that appears in many algebra...

It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines with an arbitrary value of magnetic flux can be used to create energetic barriers, which can be used to confine q...

We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field—assumed to be the real or the complex numbers—and which contains the field. Notably, we consider Fueter expansions, Gleason’s problem, the theory of hyperholomorphic rational functions, modules of Fueter series, and related pr...

We discuss how, in appropriately designed configurations, solenoids carrying a semifluxon can be used as topological energy barriers for charged quantum systems. We interpret this phenomenon as a consequence of the fact that such solenoids induce nodal lines in the wave function describing the charge, which on itself is a consequence of the Aharono...

We discuss how, in appropriately designed configurations, solenoids carrying a semifluxon can be used as topological energy barriers for charged quantum systems. We interpret this phenomenon as a consequence of the fact that such solenoids induce nodal lines in the wave function describing the charge, which on itself is a consequence of the Aharono...

We begin a study of Schur analysis in the setting of the Grassmann algebra when the latter is completed with respect to the 1-norm. We focus on the rational case. We start with a theorem on invertibility in the completed algebra and define a notion of positivity in this setting. We present a series of applications pertaining to Schur analysis, incl...

We associate with the Grassmann algebra a topological algebra of distributions, which allows the study of processes analogous to the corresponding free stochastic processes with stationary increments, as well as their derivatives.

We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field -- assumed to be the real or the complex numbers -- and which contains the field. Notably, we consider Fueter expansions, Gleason's problem, the theory of hyperholomorphic rational functions, modules of Fueter series, and rela...

We begin a study of Schur analysis in the setting of the Grassmann algebra, when the latter is completed with respect to the $1$-norm. We focus on the rational case. We start with a theorem on invertibility in the completed algebra, and define a notion of positivity in this setting. We present a series of applications pertaining to Schur analysis,...

We associate to the Grassmann algebra a topological algebra of distributions, which allows the study of processes analogous to the corresponding free stochastic processes with stationary increments, as well as their derivatives.

We discuss the concept of proper and improper density matrixes and we argue that this issue is of fundamental importance for the understanding of the quantum-mechanical CTC model proposed by Deutsch. We arrive at the conclusion that under a realistic interpretation, the distinction between proper and improper density operators is not a relativistic...

We discuss the ontological status of density matrix concept and we advance the argument that this issue is of fundamental importance to the understanding of the quantum mechanical CTC model proposed by Deutsch. We arrive at the conclusion that under a realistic interpretation, the distinction between proper and improper density operators is not rel...