Quantum Reports

11 pages, 942 KiB

Open AccessArticle

Cyclic Six-Atomic Boron-Nitrides: Quantum-Chemical Consideration by Ab Initio CCSD(T) Method

by Denis V. Chachkov and Oleg V. Mikhailov

Quantum Rep. 2022, 4(3), 351-361; https://doi.org/10.3390/quantum4030025 - 16 Sep 2022

Cited by 1 | Viewed by 1999

By means of the CCSD(T)/6-311++G(df,p) and G4 quantum-chemical calculation methods, the calculation of the molecular and electronic structures of boron–nitrogen compounds having the B₃N₃ composition was carried out and its results were discussed. It was noted that seven isomeric forms [...] Read more.

By means of the CCSD(T)/6-311++G(df,p) and G4 quantum-chemical calculation methods, the calculation of the molecular and electronic structures of boron–nitrogen compounds having the B₃N₃ composition was carried out and its results were discussed. It was noted that seven isomeric forms with different space structures can exist; wherein, the most stable form is a distorted flat hexagon with alternating B and N atoms, with both B and N atoms forming regular triangles, but with different side lengths. The values of geometric parameters of molecular structures in each of these compounds are presented. Also, the key thermodynamic parameters of formation (enthalpy Δ_fH⁰, entropy S⁰, Gibbs’ energy Δ_fG⁰) and relative total energies of these compounds are calculated. Full article

(This article belongs to the Special Issue Fundamentals and Applications in Quantum Chemistry)

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13 pages, 1610 KiB

Open AccessArticle

An Overview of Basis Set Effects for Diatomic Boron Nitride Compounds (B₂N⁽^∓^,0)): A Quantum Symmetry Breaking

by Majid Monajjemi, Fatemeh Mollaamin and Neda Samiei Soofi

Quantum Rep. 2022, 4(3), 338-350; https://doi.org/10.3390/quantum4030024 - 8 Sep 2022

Cited by 1 | Viewed by 1882

Abstract

The symmetry breaking (SB) of B₂ not only exhibits an energy barrier for ionic or neutral forms dependent on various basis sets but it also exhibits a few SBs due to the asymmetry stretching and bending mode interactions. SB obeys the mechanical [...] Read more.

The symmetry breaking (SB) of B₂ not only exhibits an energy barrier for ionic or neutral forms dependent on various basis sets but it also exhibits a few SBs due to the asymmetry stretching and bending mode interactions. SB obeys the mechanical quantum theorem among discrete symmetries and their connection to the spin statistics in physical sciences. In this investigation, the unusual amount of energy barrier of SBs appeared upon the orbit–orbit coupling of BNB (both radical and ions) between transition states and the ground state. Our goal in this study is to understand the difference among the electromagnetic structures of the (B₂N⁽^∓^,0)) variants due to effects of various basis sets and methods and also the quantum symmetry breaking phenomenon. In the D_∞h point group of (B₂N⁽^∓^,0)) variants, the unpaired electron is delocalized, while in the asymmetric C_∞v point group, it is localized on either one of the B atoms. Structures with broken symmetry, C_∞v, can be stable by interacting with the D_∞h point group. In viewpoints of quantum chemistry, the second-order Jahn–Teller effect permits the unpaired electron to localize on boron atom, rather than being delocalized. In this study, we observed that the energy barrier of SB for BNB increases by post HF methods. Full article

(This article belongs to the Special Issue Fundamentals and Applications in Quantum Chemistry)

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14 pages, 326 KiB

Open AccessArticle

Simultaneity and Time Reversal in Quantum Mechanics in Relation to Proper Time

by Salim Yasmineh

Quantum Rep. 2022, 4(3), 324-337; https://doi.org/10.3390/quantum4030023 - 8 Sep 2022

Viewed by 2331

Abstract

In Newtonian physics, the equation of motion is invariant when the direction of time (

t \to - t

) is flipped. However, in quantum physics, flipping the direction of time changes the sign of the Schrödinger equation. An anti-unitary operator is needed [...] Read more.

In Newtonian physics, the equation of motion is invariant when the direction of time (

t \to - t

) is flipped. However, in quantum physics, flipping the direction of time changes the sign of the Schrödinger equation. An anti-unitary operator is needed to restore time reversal in quantum physics, but this is at the cost of not having a consistent definition of time reversal applicable to all fundamental theories. On the other hand, a quantum system composed of a pair of entangled particles behaves in such a manner that when the state of one particle is measured, the second particle ‘simultaneously’ acquires a determinate state. A notion of absolute simultaneity seems to be inferred by quantum mechanics, even though it is forbidden by the postulates of relativity. We aim to point out that the above two problems can be overcome if the wavefunction is defined with respect to proper time, which in fact is the real physical time instead of ordinary time. Full article

15 pages, 376 KiB

Open AccessArticle

Displaced Harmonic Oscillator V ∼ min [(x + d)², (x − d)²] as a Benchmark Double-Well Quantum Model

by Miloslav Znojil

Quantum Rep. 2022, 4(3), 309-323; https://doi.org/10.3390/quantum4030022 - 24 Aug 2022

Cited by 3 | Viewed by 2199

Abstract

For the displaced harmonic double-well oscillator, the existence of exact polynomial bound states at certain displacements

d

is revealed. The N-plets of these quasi-exactly solvable (QES) states are constructed in closed form. For non-QES states, the Schrödinger equation can still be considered [...] Read more.

For the displaced harmonic double-well oscillator, the existence of exact polynomial bound states at certain displacements

d

is revealed. The N-plets of these quasi-exactly solvable (QES) states are constructed in closed form. For non-QES states, the Schrödinger equation can still be considered “non-polynomially exactly solvable” (NES) because the exact left and right parts of the wave function (proportional to confluent hypergeometric function) just have to be matched in the origin. Full article

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13 pages, 6030 KiB

Open AccessArticle

Schrödinger Equation with Geometric Constraints and Position-Dependent Mass: Linked Fractional Calculus Models

by Ervin K. Lenzi, Luiz R. Evangelista, Haroldo V. Ribeiro and Richard L. Magin

Quantum Rep. 2022, 4(3), 296-308; https://doi.org/10.3390/quantum4030021 - 14 Aug 2022

Cited by 3 | Viewed by 1778

Abstract

We investigate the solutions of a two-dimensional Schrödinger equation in the presence of geometric constraints, represented by a backbone structure with branches, by taking a position-dependent effective mass for each direction into account. We use Green’s function approach to obtain the solutions, which [...] Read more.

We investigate the solutions of a two-dimensional Schrödinger equation in the presence of geometric constraints, represented by a backbone structure with branches, by taking a position-dependent effective mass for each direction into account. We use Green’s function approach to obtain the solutions, which are given in terms of stretched exponential functions. The results can be linked to the properties of the system and show anomalous spreading for the wave packet. We also analyze the interplay between the backbone structure with branches constraining the different directions and the effective mass. In particular, we show how a fractional Schrödinger equation emerges from this scenario. Full article

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19 pages, 479 KiB

Open AccessArticle

Electromagnetic Signatures of Possible Charge Anomalies in Tunneling

by Fernando Minotti and Giovanni Modanese

Quantum Rep. 2022, 4(3), 277-295; https://doi.org/10.3390/quantum4030020 - 11 Aug 2022

Cited by 3 | Viewed by 1673

Abstract

We reconsider some well-known tunneling processes from the point of view of Aharonov-Bohm electrodynamics, a unique extension of Maxwell’s theory which admits charge-current sources that are not locally conserved. In particular we are interested into tunneling phenomena having relatively long range (otherwise the [...] Read more.

We reconsider some well-known tunneling processes from the point of view of Aharonov-Bohm electrodynamics, a unique extension of Maxwell’s theory which admits charge-current sources that are not locally conserved. In particular we are interested into tunneling phenomena having relatively long range (otherwise the non-Maxwellian effects become irrelevant, especially at high frequency) and involving macroscopic wavefunctions and coherent matter, for which it makes sense to evaluate the classical e.m. field generated by the tunneling particles. For some condensed-matter systems, admitting discontinuities in the probability current is a possible way of formulating phenomenological models. In such cases, the Aharonov-Bohm theory offers a logically consistent approach and allows to derive observable consequences. Typical e.m. signatures of the failure of local conservation are at high frequency the generation of a longitudinal electric radiation field, and at low frequency a small effect of “missing” magnetic field. Possible causes of this failure are instant tunneling and phase slips in superconductors. For macroscopic quantum systems in which the phase-number uncertainty relation

Δ N Δ φ \sim 1

applies, the expectation value of the anomalous source

I = \partial_{t} ρ + \nabla \cdot j

has quantum fluctuations, thus becoming a random source of weak non-Maxwellian fields. Full article

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5 pages, 674 KiB

Open AccessBrief Report

Equal Radiation Frequencies from Different Transitions in the Non-Relativistic Quantum Mechanical Hydrogen Atom

by Tuan K. Do and Trung V. Phan

Quantum Rep. 2022, 4(3), 272-276; https://doi.org/10.3390/quantum4030019 - 5 Aug 2022

Viewed by 1897

Abstract

Is it possible that two different transitions in the non-relativistic quantum mechanical model of the hydrogen atom give the same frequency of radiation? That is, can different energy level transitions in a hydrogen atom have the same photon radiation frequency? This question, which [...] Read more.

Is it possible that two different transitions in the non-relativistic quantum mechanical model of the hydrogen atom give the same frequency of radiation? That is, can different energy level transitions in a hydrogen atom have the same photon radiation frequency? This question, which was asked during a Ph.D. oral exam in 1997 at the University of Colorado Boulder, is well-known among physics graduate students. We show a general solution to this question, in which all equifrequency transition pairs can be obtained from the set of solutions of a Diophantine equation. This fun puzzle is a simple yet concrete example of how number theory can be relevant to quantum systems, a curious theme that emerges in theoretical physics but is usually inaccessible to a general audience. Full article

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8 pages, 663 KiB

Open AccessFeature PaperArticle

Why the Many-Worlds Interpretation?

by Lev Vaidman

Quantum Rep. 2022, 4(3), 264-271; https://doi.org/10.3390/quantum4030018 - 4 Aug 2022

Cited by 8 | Viewed by 5193

Abstract

A brief (subjective) description of the state of the art of the many-worlds interpretation of quantum mechanics (MWI) is presented. It is argued that the MWI is the only interpretation which removes action at a distance and randomness from quantum theory. Limitations of [...] Read more.

A brief (subjective) description of the state of the art of the many-worlds interpretation of quantum mechanics (MWI) is presented. It is argued that the MWI is the only interpretation which removes action at a distance and randomness from quantum theory. Limitations of the MWI regarding questions of probability which can be legitimately asked are specified. The ontological picture of the MWI as a theory of the universal wave function decomposed into a superposition of world wave functions, the important parts of which are defined in three-dimensional space, is presented from the point of view of our particular branch. Some speculations about misconceptions, which apparently prevent the MWI from being in the consensus, are mentioned. Full article

(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)

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<bold>Measurement problem.</bold> (<bold>a</bold>) The detection of a single photon is fully understood by the creation of a particular quantum wave of parts of the single-photon detector. (<bold>b</bold>) In the experiment with a single-photon source, beamsplitter, and two detectors, the quantum mechanical equations show a similar (although reduced) change in two detectors. Nevertheless, we never observe simultaneous clicks of the two detectors. Full article ">Figure 2
<bold>Action at a distance in a single-world universe.</bold> If we do nothing at <italic>A</italic>, then at a particular moment, there will be probability <inline-formula><mml:math id="mm2"><mml:semantics><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn></mml:mrow></mml:semantics></mml:math></inline-formula> of finding a photon at a spacelike separated region <italic>B</italic>. Introducing a detector just before <italic>A</italic> will lead to a superluminal change in <italic>B</italic> to <inline-formula><mml:math id="mm3"><mml:semantics><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:semantics></mml:math></inline-formula> or <inline-formula><mml:math id="mm4"><mml:semantics><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:semantics></mml:math></inline-formula>. The change will not be known immediately at <italic>B</italic>, but it does not change the fact that something in <italic>B</italic> changed, e.g., the readiness of an agent in <italic>A</italic> to bet about the result of an experiment in <italic>B</italic>. Full article ">Figure 3
<bold>The world structure in the MWI and a single-world universe.</bold> (<bold>a</bold>) The whole tree of many worlds in the MWI. (<bold>b</bold>) One world of the MWI until present together with the tree of future worlds splitting out of it in the future. (<bold>c</bold>) One of the corresponding worlds of the theory with collapse. Full article ">

13 pages, 703 KiB

Open AccessFeature PaperArticle

End-to-End Entanglement Generation Strategies: Capacity Bounds and Impact on Quantum Key Distribution

by Antonio Manzalini and Michele Amoretti

Quantum Rep. 2022, 4(3), 251-263; https://doi.org/10.3390/quantum4030017 - 29 Jul 2022

Cited by 8 | Viewed by 2618

Abstract

A first quantum revolution has already brought quantum technologies into our everyday life for decades: in fact, electronics and optics are based on the quantum mechanical principles. Today, a second quantum revolution is underway, leveraging the quantum principles of superposition, entanglement and measurement, [...] Read more.

A first quantum revolution has already brought quantum technologies into our everyday life for decades: in fact, electronics and optics are based on the quantum mechanical principles. Today, a second quantum revolution is underway, leveraging the quantum principles of superposition, entanglement and measurement, which were not fully exploited yet. International innovation activities and standardization bodies have identified four main application areas for quantum technologies and services: quantum secure communications, quantum computing, quantum simulation, and quantum sensing and metrology. This paper focuses on quantum secure communications by addressing the evolution of Quantum Key Distribution (QKD) networks (under early exploitation today) towards the Quantum-ready networks and the Quantum Internet based also on entanglement distribution. Assuming that management and control of quantum nodes is a key challenge under definition, today, a main obstacle in exploiting long-range QKD and Quantum-ready networks concerns the inherent losses due to the optical transmission channels. Currently, it is assumed that a most promising way for overcoming this limitation, while avoiding the presence of costly trusted nodes, it is to distribute entangled states by means of Quantum Repeaters. In this respect, the paper provides an overview of current methods and systems for end-to-end entanglement generation, with some simulations and a discussion of capacity upper bounds and their impact of secret key rate in QKD systems. Full article

(This article belongs to the Special Issue From Quantum Networks to Quantum Internet: Opportunities and Challenges)

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13 pages, 5073 KiB

Open AccessArticle

Non-Relativistic Energy Spectra of the Modified Hylleraas Potential and Its Thermodynamic Properties in Arbitrary Dimensions

by Collins Okon Edet, Jonathan E. Osang, Norshamsuri Ali, Emmanuel Paul Agbo, Syed Alwee Aljunid, Rosdisham Endut, Emmanuel B. Ettah, Reza Khordad, Akpan Ndem Ikot and Muhammad Asjad

Quantum Rep. 2022, 4(3), 238-250; https://doi.org/10.3390/quantum4030016 - 29 Jul 2022

Cited by 3 | Viewed by 1940

Abstract

In this study, the solutions of the Schrodinger equation (SE) with modified Hylleraas potential in arbitrary dimensions was obtained using the asymptotic iteration method (AIM) to obtain the energy and wave functions, respectively. The energy equation was used to obtain the thermal properties [...] Read more.

In this study, the solutions of the Schrodinger equation (SE) with modified Hylleraas potential in arbitrary dimensions was obtained using the asymptotic iteration method (AIM) to obtain the energy and wave functions, respectively. The energy equation was used to obtain the thermal properties of this system. The effect of the potential parameters and dimensions on the energy spectra and thermal properties was scrutinized thoroughly. It was found that the aforementioned affects the thermal properties and energy spectra, respectively. In addition, we also computed the numerical energy spectra of the MHP for the first time and discussed it in detail. The results of our study can be applied to molecular physics, chemical physics, etc. Full article

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17 pages, 1128 KiB

Open AccessArticle

Entanglement in Quantum Search Database: Periodicity Variations and Counting

by Demosthenes Ellinas and Christos Konstandakis

Quantum Rep. 2022, 4(3), 221-237; https://doi.org/10.3390/quantum4030015 - 22 Jul 2022

Viewed by 1550

Abstract

Employing the single item search algorithm of N dimensional database it is shown that: First, the entanglement developed between two any-size parts of database space varies periodically during the course of searching. The periodic entanglement of the associated reduced density matrix quantified by [...] Read more.

Employing the single item search algorithm of N dimensional database it is shown that: First, the entanglement developed between two any-size parts of database space varies periodically during the course of searching. The periodic entanglement of the associated reduced density matrix quantified by several entanglement measures (linear entropy, von Neumann, Renyi), is found to vanish with period

O (s q r t (N))

. Second, functions of equal entanglement are shown to vary also with equal period. Both those phenomena, based on size-independent database bi-partition, manifest a general scale invariant property of entanglement in quantum search. Third, measuring the entanglement periodicity via the number of searching steps between successive canceling out, determines N, the database set cardinality, quadratically faster than ordinary counting. An operational setting that includes an Entropy observable and its quantum circuits realization is also provided for implementing fast counting. Rigging the marked item initial probability, either by initial advice or by guessing, improves hyper-quadratically the performance of those phenomena. Full article

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Quantum Rep., Volume 4, Issue 3 (September 2022) – 11 articles

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