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Results for “POSITION OPERATORS”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
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DOE OSTI2015

A new look at the position operator in quantum theory

The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory by analogy with classical electrodynamics. As a consequence, an inevitable effect in standard theory is the wave packet spreading (WPS) of the photon coordinate wave function in directions perpendicular to the photon momentum. This leads to the following paradoxes: if the major part of photons emitted by stars are in wave packet states (what is the most probable scenario) then we should see not separate stars but only an almost continuous background from all stars; no anisotropy of the CMB radiation should be observable; data on gamma-ray bursts, signals from directional radio antennas (in particular, in experiments on Shapiro delay) and signals from pulsars show no signs of WPS. In addition, a problem arises why there are no signs of WPS for protons in the LHC ring. We argue that the above postulate is based neither on strong theoretical arguments nor on experimental data and propose a new consistent definition of the position operator. Then WPS in directions perpendicular to the particle momentum is absent and the paradoxes are resolved. Different components of the new position operator do not commute with each other and, as a consequence, there is no wave function in coordinate representation. Implications of the results for entanglement, quantum locality and the problem of time in quantum theory are discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Minimal sufficient positive-operator valued measure on a separable Hilbert space

We introduce a concept of a minimal sufficient positive-operator valued measure (POVM), which is the least redundant POVM among the POVMs that have the equivalent information about the measured quantum system. Assuming the system Hilbert space to be separable, we show that for a given POVM, a sufficient statistic called a Lehmann-Scheffé-Bahadur statistic induces a minimal sufficient POVM. We also show that every POVM has an equivalent minimal sufficient POVM and that such a minimal sufficient POVM is unique up to relabeling neglecting null sets. We apply these results to discrete POVMs and information conservation conditions proposed by the author.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Position Operators in Terms of Converging Finite-Dimensional Matrices and Their Intertwining with Geometry, Transport, and Gauge

The position operator 𝑟̂ appears as 𝑖∂ 𝑝 in wave mechanics, while its matrix form (e.g., under a Bloch basis) is well known diverging in diagonals, causing difficulties in basis transformation, observable yielding, etc. We aim to find a convergent r-matrix (CRM) to improve the existing divergent r-matrix (DRM), and investigate its influence at both the conceptual and the application levels. A key modification is increasing the familiar substitution of 𝑟̂ by 𝑖∂ 𝑝 to 𝑖∑ 𝑗 ∂ 𝑘 𝑗 , namely the N-th Weyl algebra. Resolving the divergence makes r-matrix rigorously defined, and we are able to show r-matrix is distinct from a spin matrix in terms of its defining principles, transformation behavior, and the observable it yields. Conceptually, the CRM fills the logical gap between the r-matrix and the Berry connection (this unremarked vagueness has caused the diagonal divergence). In application, we focus on transport, and discover that the Hermitian matrix is not identical with the associative Hermitian operator, i.e., 𝑟 𝑚,𝑛 = 𝑟$^∗_{𝑛,𝑚}$ ⇎ 𝑟̂ = 𝑟̂ † , which subtly affects the celebrated Berry curvature formula for adiabatic current. We also discuss how such a non-representation CRM can contribute to building a unified transport theory.

Weyl algebras↗
DOE OSTI2023

Perturbation theory for the logarithm of a positive operator

In various contexts in mathematical physics, such as out-of-equilibrium physics and the asymptotic information theory of many-body quantum systems, one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the Tomita-Takesaki theory. Often, one encounters the situation where the operator under consideration, which we denote by ∆, can be related by a perturbative series to another operator ∆ 0 , whose logarithm is known. We set up a perturbation theory for the logarithm log ∆. It turns out that the terms in the series possess a remarkable algebraic structure, which enables us to write them in the form of nested commutators plus some “contact terms”.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Algebraic function operator expectation value based quantum eigenstate determination: A case of twisted or bent Hamiltonian, or, a spatially univariate quantum system on a curved space

Recent studies on quantum evolutionary problems in Demiralp’s group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraic equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Wigner functions for noncommutative quantum mechanics: A group representation based construction

This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and those of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom

This proceedings paper aims to show the efficiency of an expectation value identity for a given algebraic function operator which is assumed to be depending pn only position operator. We show that this expectation value formula becomes enabled to determine the eigenstates of the quantum system Hamiltonian as long as it is autonomous and an appropriate basis set in position operator is used. This approach produces a denumerable infinite recursion which may be considered as revisited but at the same time generalized form of the recursions over the natural number powers of the position operator. The content of this short paper is devoted not only to the formulation of the new method but also to show that this novel approach is capable of catching the eigenvalues and eigenfunctions for Hydrogen-like systems, beyond that, it can give a hand to us to reveal the wavefunction structure. So it has also somehow a confirmative nature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Conformal, wearable, thin microwave antenna for sub-skin and skin surface monitoring

A wearable antenna is operably positioned on a wearer's skin and is operably connected the wearer's tissue. A first antenna matched to the wearer's tissue is operably positioned on the wearer's skin. A second antenna matched to the air is operably positioned on the wearer's skin. Transmission lines connect the first antenna and the second antenna.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Energy recovery ventilator

An energy recovery heat exchanger (100) includes a housing (102). The housing has a first flowpath (144) from a first inlet (104) to a first outlet (106). The housing has a second flowpath (146) from a second inlet (108) to a second outlet (110). Either of two cores may be in an operative position in the housing. Each core has a number of first passageways having open first and second ends and closed first and second sides. Each core has a number of second such passageways interspersed with the first passageways. The ends of the second passageways are aligned with the sides of the first passageways and vice versa. A number of heat transfer member sections separate adjacent ones of the first and second passageways. An actuator is coupled to the carrier to shift the cores between first and second conditions. In the first condition, the first core (20) is in the operative position and the second core (220) is not. In the second condition, the second core is in the operative position and the first core is not. When a core is in the operative position, its first passageways are along the first flowpath and the second passageways are along the second flowpath.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2014

Extended space expectation values of position related operators for hydrogen-like quantum system evolutions

The expectation value definitions over an extended space from the considered Hilbert space of the system under consideration is given in another paper of the second author in this symposium. There, in that paper, the conceptuality rather than specification is emphasized on. This work uses that conceptuality to investigate the time evolutions of the position related operators' expectation values not in its standard meaning but rather in a new version of the definition over not the original Hilbert space but in the space obtained by extensions via introducing the images of the given initial wave packet under the positive integer powers of the system Hamiltonian. These images may not be residing in the same space of the initial wave packet when certain singularities appear in the structure of the system Hamiltonian. This may break down the existence of the integrals in the definitions of the expectation values. The cure is the use of basis functions in the abovementioned extended space and the sandwiching of the target operator whose expectation value is under questioning by an appropriately chosen operator guaranteeing the existence of the relevant integrals. Work specifically focuses on the hydrogen-like quantum systems whose Hamiltonians contain a polar singularity at the origin.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A conformal collider for holographic CFTs

We develop a formalism to study the implications of causality on OPE coefficients in conformal field theories with large central charge and a sparse spectrum of higher spin operators. The formalism has the interpretation of a new conformal collider-type experiment for these class of CFTs and hence it has the advantage of requiring knowledge only about CFT three-point functions. This is accomplished by considering the holographic null energy operator which was introduced in [ 1 ] as a generalization of the averaged null energy operator. Analyticity properties of correlators in the Regge limit imply that the holographic null energy operator is a positive operator in a subspace of the total CFT Hilbert space. Utilizing this positivity condition, we derive bounds on three-point functions $\langle$ TO 1 O 2 $\rangle$of the stress tensor with various operators for CFTs with large central charge and a sparse spectrum. After imposing these constraints, we also find that the operator product expansions of all primary operators in the Regge limit have certain universal properties. All of these results are consistent with the expectation that CFTs in this class, irrespective of their microscopic details, admit universal gravity-like holographic dual descriptions. Furthermore, this connection enables us to constrain various inflationary observables such as the amplitude of chiral gravity waves, non-gaussanity of gravity waves and tensor-to-scalar ratio.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Relativistic dynamics, Green function and pseudodifferential operators

The central role played by pseudodifferential operators in relativistic dynamics is known very well. In this work, operators like the Schrodinger one (e.g., square root) are treated from the point of view of the non-local pseudodifferential Green functions. Starting from the explicit construction of the Green (semigroup) theoretical kernel, a theorem linking the integrability conditions and their dependence on the spacetime dimensions is given. Relativistic wave equations with arbitrary spin and the causality problem are discussed with the algebraic interpretation of the radical operator and their relation with coherent and squeezed states. Also we perform by means of pure theoretical procedures (based in physical concepts and symmetry) the relativistic position operator which satisfies the conditions of integrability: it is a non-local, Lorentz invariant and does not have the same problems as the “local”position operator proposed by Newton and Wigner. Physical examples, as zitterbewegung and rogue waves, are presented and deeply analyzed in this theoretical framework.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Factorization method for Schrödinger equation in relativistic configuration space and q-deformations

Review paper is devoted to the relativistic configuration space (RCS) concept, a version of the relativistic Quantum Mechanics in RCS, the generalization of the Dirac-Infeld-Hall factorization method in the framework of the noncommutative differential calculus natural for RCS, different versions of the deformed oscillators, emerging as the generalization of the harmonic oscillator for RCS. In the formulation of the Newton-Wigner postulates for the relativistic localized states the hypothesis of commutativity of the position operator components is silently accepted as an evident fact. In the present work it is shown that commutativity is not necessary condition and the alternative (noncommutative) approach to the relativistic position operator and localization concept can be realized in a framework of the physically as well as mathematically comprehensive scheme. The different generalizations of the Dirac-Infeld-Hall factorization method for this case are constructed. This method enables us to find out all possible generalizations of the most important nonrelativistic integrable case—the harmonic oscillator. It is shown also that the relativistic oscillator = q —oscillator.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Localizability, gauge symmetry and Newton–Wigner operator for massless particles

The notion of position operator for massless spinning particles is discussed in some detail. The noncommutativity of coordinates is related to the gauge symmetry following from the freedom in definition of standard state in Wigner’s construction of induced representations of Poincare group. The counterpart of Newton–Wigner operator is discussed. It is explained why the Newton–Wigner construction works only for helicity |λ|≤1∕2.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Time reversal symmetry of generalized quantum measurements with past and future boundary conditions

Here we expand the time reversal symmetry arguments of quantum mechanics, originally proposed by Wigner in the context of unitary dynamics, to contain situations including generalized measurements for monitored quantum systems. We propose a scheme to derive the time-reversed measurement operators by considering the Schrödinger picture dynamics of a qubit coupled to a measuring device, and show that the time-reversed measurement operators form a Positive Operator Valued Measure (POVM) set. We present three particular examples to illustrate time reversal of measurement operators: (1) the Gaussian spin measurement, (2) a dichotomous POVM for spin, and (3) the measurement of qubit fluorescence. We then propose a general rule to unravel any rank two qubit measurement, and show that the backward dynamics obeys the retrodicted equations of the forward dynamics starting from the time reversed final state. We demonstrate the time reversal invariance of dynamical equations using the example of qubit fluorescence. We also generalize the discussion of a statistical arrow of time for continuous quantum measurements introduced by Dressel et al. (Phys Rev Lett 119:220507, 2017): we show that the backward probabilities can be computed from a process similar to retrodiction from the time-reversed final state, and extend the definition of an arrow of time to ensembles prepared with pre- and post-selections, where we obtain a non-vanishing arrow of time in general. We discuss sufficient conditions for when time’s arrow vanishes and show our method also captures the contributions to time’s arrow due to natural physical processes like relaxation of an atom to its ground state. As a special case, we recover the time reversibility of the weak value as its complex conjugate using our method, and discuss how our conclusions differ from the time-symmetry argument of Aharonov–Bergmann–Lebowitz rule.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Causal localizations in relativistic quantum mechanics

Causal localizations describe the position of quantum systems moving not faster than light. They are constructed for the systems with finite spinor dimension. At the center of interest are the massive relativistic systems. For every positive mass, there is the sequence of Dirac tensor-localizations, which provides a complete set of inequivalent irreducible causal localizations. They obey the principle of special relativity and are fully Poincaré covariant. The boosters are determined by the causal position operator and the other Poincaré generators. The localization with minimal spinor dimension is the Dirac localization. Thus, the Dirac equation is derived here as a mere consequence of the principle of causality. Moreover, the higher tensor-localizations, not known so far, follow from Dirac’s localization by a simple construction. The probability of localization for positive energy states results to be described by causal positive operator valued (PO-) localizations, which are the traces of the causal localizations on the subspaces of positive energy. These causal Poincaré covariant PO-localizations for every irreducible massive relativistic system were, all the more, not known before. They are shown to be separated. Hence, the positive energy systems can be localized within every open region by a suitable preparation as accurately as desired. Finally, the attempt is made to provide an interpretation of the PO-localization operators within the frame of conventional quantum mechanics attributing an important role to the negative energy states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Carbon fuel cells with carbon corrosion suppression

An electrochemical cell apparatus that can operate as either a fuel cell or a battery includes a cathode compartment, an anode compartment operatively connected to the cathode compartment, and a carbon fuel cell section connected to the anode compartment and the cathode compartment. An effusion plate is operatively positioned adjacent the anode compartment or the cathode compartment. The effusion plate allows passage of carbon dioxide. Carbon dioxide exhaust channels are operatively positioned in the electrochemical cell to direct the carbon dioxide from the electrochemical cell.

25 ENERGY STORAGE↗