Terms Of Quantum Mechanics Research Articles

The GRW Flash Theory: A Relativistic Quantum Ontology of Matter in Space-Time?

John Bell proposed an ontology for the GRW (Ghirardi, Rimini, and Weber) modification of quantum mechanics in terms of flashes occurring at space-time points. This article spells out the motivation for this ontology, inquires into the status of the wave function in it, critically examines the claim of its being Lorentz invariant, and considers whether it is a parsimonious but nevertheless physically adequate ontology.

Thinking carefully about quantum information

The development of quantum information theory over the last 20 years has produced a plethora of interesting new results and along with them a host of claims have been made by physicists and philosophers about how quantum information theory helps us understand the quantum world. When one examines such claims with any attention to detail, it is quite obvious that radically different and incompatible claims are being made about the quantum world. Christopher Timpson’s Quantum Information Theory and the Foundations of Quantum Mechanics provide a sober and thorough critical guide to these claims. Claims made about how quantum information theory can help us understand the quantum world are a motley collection, and so too are the chapters of Timpson’s book. That said, they can almost be sorted into two broad categories: those that aim to define quantum information and to understand the quantum world in terms of it, and those that aim to reconstruct quantum mechanics in terms of informationtheoretic axioms which will render the quantum world understandable to us. Timpson’s Chapter 6, on quantum computation is the exception. Oftentimes, different concepts of information are deployed in the literature associated with quantum information theory that are as much related as Michael Jackson the pop music icon and Michael Jackson the beer and whisky expert. It is strikingly ironic how much confusion has been generated by appeal to concepts of information. Timpson’s second chapter, ‘‘What is information?’’, is the antidote to such confusion. Timpson claims that there are really only two proper ways to talk about information in this context: the everyday way, which has a strong connection to knowledge, and the technical way, whose roots lie in Shannon (1948). With respect to both, Timpson’s most pressing point is to guard against a view that

Tunnel magnetoresistance in asymmetric double-barrier magnetic tunnel junctions

Abstract The spin-polarized tunnel conductance and tunnel magnetoresistance (TMR) through a planar asymmetric double-barrier magnetic tunnel junction (DBMTJ) have been calculated using quasi-classical model. In DBMTJ nanostructure the magnetization of middle ferromagnetic metal layer can be aligned parallel or antiparallel with respect to the fixed magnetizations of the top and bottom ferromagnetic electrodes. The transmission coefficients of an electron to pass through the barriers have been calculated in terms of quantum mechanics. The dependencies of tunnel conductance and TMR on the applied voltage have been calculated in case of non-resonant transmission. Estimated in the framework of our model, the difference between the spin-channels conductances at low voltages was found relatively large. This gives rise to very high magnitude of TMR.

Riemann surface dynamics of periodic non-Hermitian Hamiltonians

A number of physical problems, including statistical mechanics of 1D multivalent Coulomb gases, may be formulated in terms of non-Hermitian quantum mechanics. We use this example to develop a non-perturbative method of instanton calculus for non-Hermitian Hamiltonians. This can be seen as an extension of semiclassical methods in conventional quantum mechanics. Treating momentum and coordinate as complex variables yields a Riemann surface of constant complex energy. The classical and instanton actions are given by periods of this surface; we show how to obtain these via methods from algebraic topology. We demonstrate the accuracy of this analytic procedure in comparison with numerical simulations for a class of periodic non-Hermitian Hamiltonians, as well as the validity of the Bohr–Sommerfeld quantization and Gamow's formula in these cases.

THE STATIC STRING

In this paper, the quantum fluctuation of a rigid and static string is reported to be identical to a free quantum particle. Solutions similar to this static string have already been found in the semiclassical quantization of pulsating strings, and our results show that the semiclassical quantization of pulsating strings is, in some cases, a perturbation of static strings. We also interpret the energy of the static string as a lower bound for the pulsating string and speculate about a description of quantum mechanics in terms of semiclassical string theory.

A General No-Cloning Theorem for an infinite Multiverse

In this paper, I formulate a general no-cloning theorem which covers the quantum-mechanical and the theoretical quantum information cases as well as the cosmological multiverse theory. However, the main argument is topological and does not involve the peculiar copier devices of the quantum-mechanical and information-theoretic approaches to the no-cloning thesis. It is shown that a combinatorial set-theoretic treatment of the mathematical and physical spacetime continuum in cosmological or quantum-mechanical terms forbids an infinite (countable or uncountable) number of exact copies of finite elements (states) in the uncountable multiverse cosmology. The historical background draws on ideas from Weyl to Conway and Kochen on the free will theorem in quantum mechanics .

PROLIFERATION OF OBSERVABLES AND MEASUREMENT IN QUANTUM-CLASSICAL HYBRIDS

Following a review of quantum-classical hybrid dynamics, we discuss the ensuing proliferation of observables and relate it to measurements of (would-be) quantum mechanical degrees of freedom performed by (would-be) classical ones (if they were separable). Hybrids consist in coupled classical (CL) and quantum mechanical (QM) objects. Numerous consistency requirements for their description have been discussed and are fulfilled here. We summarize a representation of quantum mechanics in terms of classical analytical mechanics which is naturally extended to QM–CL hybrids. This framework allows for superposition, separable, and entangled states originating in the QM sector, admits experimenter's "Free Will", and is local and nonsignaling. Presently, we study the set of hybrid observables, which is larger than the Cartesian product of QM and CL observables of its components; yet it is smaller than a corresponding product of all-classical observables. Thus, quantumness and classicality infect each other.

Inter-dimensional effects in nano-structures

We report on two extensions of the traditional analysis of low-dimensional structures in terms of low-dimensional quantum mechanics. On one hand, we discuss the impact of thermodynamics in one or two dimensions on the behavior of fermions in low-dimensional systems. On the other hand, we use both quantum wells and interfaces with different effective electron or hole mass to study the question when charge carriers in interfaces or layers exhibit two-dimensional or three-dimensional behavior. We find in particular that systems with different effective masses in the bulk and in the interface exhibit separation of two-dimensional and three-dimensional behavior on different length scales, whereas quantum wells exhibit linear combination of two-dimensional and three-dimensional behavior on short length scales while the behavior on large length scales cannot be associated with either two-dimensional or three-dimensional behavior.

COMPUTATION OF QUANTUM ELECTRICAL CURRENTS THROUGH THE RAMO–SHOCKLEY–PELLEGRINI THEOREM WITH TRAJECTORIES

Motivated by a recent approach to solve quantum dynamics with full Coulomb correlations [X. Oriols, Phys. Rev. Lett.98 (2007) 066803], we present here an extension of the Ramo–Shockley–Pellegrini theorem for quantum systems to compute the total (conduction plus displacement) current in terms of quantum (Bohmian) trajectories. By way of test, we derive an extension of the Ramo-Shockley-Pellegrini theorem using standard quantum mechanics and we compare it to our former result. As expected, both formulations give identical results, however we emphasize the numerical viability of computing self-consistently the total current by means of quantum trajectories in front of the difficulties to do it in terms of standard quantum mechanics.

Complex Riccati equations as a link between different approaches for the description of dissipative and irreversible systems

Quantum mechanics is essentially described in terms of complex quantities like wave functions. The interesting point is that phase and amplitude of the complex wave function are not independent of each other, but coupled by some kind of conservation law. This coupling exists in time-independent quantum mechanics and has a counterpart in its time-dependent form. It can be traced back to a reformulation of quantum mechanics in terms of nonlinear real Ermakov equations or equivalent complex nonlinear Riccati equations, where the quadratic term in the latter equation explains the origin of the phase-amplitude coupling. Since realistic physical systems are always in contact with some kind of environment this aspect is also taken into account. In this context, different approaches for describing open quantum systems, particularly effective ones, are discussed and compared. Certain kinds of nonlinear modifications of the Schrödinger equation are discussed as well as their interrelations and their relations to linear approaches via non-unitary transformations. The modifications of the aforementioned Ermakov and Riccati equations when environmental effects are included can be determined in the time-dependent case. From formal similarities conclusions can be drawn how the equations of time-independent quantum mechanics can be modified to also incluce the enviromental aspects.

Molecular mechanical perspective on halogen bonding

The nature and strength of halogen bonding in halo molecule-Lewis base complexes were studied in terms of molecular mechanics using our recently developed positive extra-point (PEP) approach, in which the σ-hole on the halogen atom is represented by an extra point of positive charge. The contributions of the σ-hole (i.e., positively charged extra point) and the halogen atom to the strength of this noncovalent interaction were clarified using the atomic parameter contribution to the molecular interaction (APCtMI) approach. The molecular mechanical results revealed that the halogen bond is electrostatic and van der Waals in nature, and its strength depends on three types of interaction: (1) the attractive electrostatic interaction between the σ-hole and the Lewis base, (2) the repulsive electrostatic interaction between the negative halogen atom and the Lewis base, and (3) the repulsive/attractive van der Waals interactions between the halogen atom and the Lewis base. The strength of the halogen bond increases with increasing σ-hole size (i.e., magnitude of the extra-point charge) and increasing halogen atom size. The van der Waals interaction's contribution to the halogen bond strength is most favorable in chloro complexes, whereas the electrostatic interaction is dominant in iodo complexes. The idea that the chloromethane molecule can form a halogen bond with a Lewis base was revisited in terms of quantum mechanics and molecular mechanics. Although chloromethane does produce a positive region along the C-Cl axis, basis set superposition error corrected second-order Møller-Plesset calculations showed that chloromethane-Lewis base complexes are unstable, producing halogen-Lewis base contacts longer than the sum of the van der Waals radii of the halogen and O/N atoms. Molecular mechanics using the APCtMI approach showed that electrostatic interactions between chloromethane and a Lewis base are unfavorable owing to the high negative charge on the chlorine atom, which overcomes the corresponding favorable van der Waals interactions.

Remarks on Osmosis, Quantum Mechanics, and Gravity

Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.

A New Estimate on the Two-Dimensional Indirect Coulomb Energy

We prove a new lower bound on the indirect Coulomb energy in two dimensional quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the Lieb--Solovej--Yngvason bound with a smaller constant, C=(4/3)^{3/2}\sqrt{5 \pi -1} \approx 5.90 < C_{LSY}= 192\sqrt{2 \pi} \approx 481.27, which also involves an additive gradient energy term of the single particle density.

Application of Quantum-Behaved Particle Swarm Optimization in Engineering Constrained Optimization Problems

To overcome the shortage of standard Particle Swarm Optimization(SPSO) on premature convergence, Quantum-behaved Particle Swarm Optimization (QPSO) is presented to solve engineering constrained optimization problem. QPSO algorithm is a novel PSO algorithm model in terms of quantum mechanics. The model is based on Delta potential, and we think the particle has the behavior of quanta. Because the particle doesn’t have a certain trajectory, it has more randomicity than the particle which has fixed path in PSO, thus the QPSO more easily escapes from local optima, and has more capability to seek the global optimal solution. In the period of iterative optimization, outside point method is used to deal with those particles that violate the constraints. Furthermore, compared with other intelligent algorithms, the QPSO is verified by two instances of engineering constrained optimization, experimental results indicate that the algorithm performs better in terms of accuracy and robustness.

Erratum: Mixed quantum-classical dynamics of an amide-I vibrational excitation in a proteinα-helix [Phys. Rev. B82, 174308 (2010)

In the GROMACS code modifications, instead of the nanometer unit for the distance that is standard in GROMACS, a unit of 1 A was previously assumed. This led to dipole-dipole interactions between amide I vibrations at different sites and the interaction energies of the amide I vibration with the protein hydrogen bonds being overestimated, respectively, by three orders and by one order of magnitude. In addition, the quantum mechanical force terms were overestimated because, through the same error, the sites defined as hydrogen-bonded in the protein were not properly identified. Because the influence of the quantum vibration on the conformation of the polypeptide is less pronouncedwhen these errors are corrected, the simulation times are increased to 10 ps. Moreover, each of the 20 simulation runs, obtained by varying the seed of the random number generator for the initial velocities, was repeated ten times in order to sample different quantumMonte Carlo paths and to yield better statistical estimates. Thus, the results presented here, for each value of χ , represent averages over 200 simulation trajectories. Two other changes are made in the current modified GROMACS code. The first of these makes sure that the interaction energy term varies continuously with the length of the hydrogen bond, even when the hydrogen bond breaks. This term is calculated as

Fast scramblers of small size

We investigate various geometrical aspects of the notion of `optical depth' in the thermal atmosphere of black hole horizons. Optical depth has been proposed as a measure of fast-crambling times in such black hole systems, and the associated optical metric suggests that classical chaos plays a leading role in the actual scrambling mechanism. We study the behavior of the optical depth with the size of the system and find that AdS/CFT phase transitions with topology change occur naturally as the scrambler becomes smaller than its thermal length. In the context of detailed AdS/CFT models based on D-branes, T-duality implies that small scramblers are described in terms of matrix quantum mechanics.

The role of gauge symmetry in spintronics

In this work we employ a field theoretical approach to explain the nature of the non-conserved spin current in spintronics. In particular, we consider the usual U ( 1 ) gauge theory for the electromagnetism at classical level in order to obtain the broken continuity equation involving the spin current and spin-transfer torque. Inspired by the recent work of A. Vernes, B. L. Gyorffy and P. Weinberger where they obtain such an equation in terms of relativistic quantum mechanics, we formalize their result in terms of the well known currents of field theory such as the Bargmann–Wigner current and the chiral current. Thus, an interpretation of spintronics is provided in terms of Noether currents (conserved or not) and symmetries of the electromagnetism. In fact, the main result of the present work is that the non-conservation of the spin current is associated with the gauge invariance of physical observables where the breaking term is proportional to the chiral current. Moreover, we generalize their result by including the electromagnetic field as a dynamical field instead of an external one.

Fractionation of REE in the xenotime and florencite paragenetic association from Au-REE mineral occurrences of the Nether-Polar Urals

A detailed survey of REE distribution in the xenotime and florencite paragenetic association from quartz veins of Au-REE mineral occurrences of the Nether-Polar Urals revealed maximum contents of Ce, Nd, Sm, Gd, Dy, and Y. Four of these elements form their own minerals: florencite-(Ce), -(Nd), and -(Sm) and xenotime-(Y) containing up to 25% Gd2O3. The compositions of the minerals are isomorphous mixtures of two different groups: Ybpg (Y, Ho, Er, Yb, Lu, Nd, and As) and Gdpg (Gd, Tb, Dy, Eu, and Sm) in xenotime and Lapg (La, Ce, Pr, Eu, and As) and Smpg (Nd, Sm, Gd, Sr, Ca, and S) in florencite. Both minerals display strong heterogeneities in the distribution of isomorphous components and two types of zoning, oscillatory and trend. The crystal cores are enriched in HREE. Variations in the composition of isomorphous mixtures are accompanied by a change in the dominant crystal forms of florencite. Redeposited varieties are distinguished by homogeneous composition, the absence of impurities, and weak correlations between elements. The REE fractionation is interpreted in terms of quantum mechanics.

Zoning and sectoriality of the florencite and xenotime group minerals from quartz veins, the Subpolar Urals

A detailed study of the florencite and xenotime assemblage from quartz veins of Au-REE occurrences in the Subpolar Urals allowed the REE fractionation and distribution of REE mixtures in the crystal structure to be characterized. In minerals of selective composition, isomorphic mixtures of LREE and HREE are divided into lanthanum Lasg (La-Pr) and samarium Smsg (Nd-Eu) subgroups in florencite and gadolinium Gdsg (Gd-Dy) and ytterbium Ybsg (Ho-Lu) subgroups in xenotime. Concentrations of elements from these subgroups are inversely proportional to each other. Each florencite or xenotime crystal is characterized by several mineral varieties: xenotime-(Y) and Gd-bearing xenotime-(Y), florencite-(Sm), -(Nd), and -(Ce); they are selectively distributed by growth zones and pyramids of the crystal with formation of direct and inverse zoning. In both cases, cores of the crystals are enriched in HREE. The correlation between REEs, Y, and such trace elements as As, S, Ca, Sr, U, and Sc is established. REE deportment is considered in minerals formed as products of primary crystallization and hydrothermal redeposition. The REE fractionation is interpreted in terms of quantum mechanics.

Is quantum mechanics nonlocal?

A factual inconsistency of the nonlocality theory is demonstrated via a careful analysis of the conceptual and formal contents of Bell's theorem and the inequalities associated with it. The conceptual inconsistency of the theory follows from the consideration that it is, in principle, impossible to formulate quantum mechanics in terms of local hidden variables. The formal inconsistency of the nonlocality theory follows from the facts that: (i) nonlocality is not a physical property that can be represented by a function or an operator; (ii) it is impossible to derive Bell's inequality in a mathematically consistent way; and (iii) Bell's definition of locality is incorrect. Therefore, Bell's theorem cannot serve as the foundation for the introduction of the nonlocality notion in quantum mechanics.