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At least 127 records · Page 7
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DOE OSTI2014

Casimir effect for a scalar field via Krein quantization

In this work, we present a rather simple method to study the Casimir effect on a spherical shell for a massless scalar field with Dirichlet boundary condition by applying the indefinite metric field (Krein) quantization technique. In this technique, the field operators are constructed from both negative and positive norm states. Having understood that negative norm states are un-physical, they are only used as a mathematical tool for renormalizing the theory and then one can get rid of them by imposing some proper physical conditions. -- Highlights: • A modification of QFT is considered to address the vacuum energy divergence problem. • Casimir energy of a spherical shell is calculated, through this approach. • In this technique, it is shown, the theory is automatically regularized.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Second quantized scalar QED in homogeneous time-dependent electromagnetic fields

We formulate the second quantization of a charged scalar field in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian is an infinite system of decoupled, time-dependent oscillators for electric fields, but it is another infinite system of coupled, time-dependent oscillators for magnetic fields. We then employ the quantum invariant method to find various quantum states for the charged field. For time-dependent electric fields, a pair of quantum invariant operators for each oscillator with the given momentum plays the role of the time-dependent annihilation and the creation operators, constructs the exact quantum states, and gives the vacuum persistence amplitude as well as the pair-production rate. We also find the quantum invariants for the coupled oscillators for the charged field in time-dependent magnetic fields and advance a perturbation method when the magnetic fields change adiabatically. Finally, the quantum state and the pair production are discussed when a time-dependent electric field is present in parallel to the magnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Quantization of soluble classical constrained systems

The derivation of the brackets among coordinates and momenta for classical constrained systems is a necessary step toward their quantization. Here we present a new approach for the determination of the classical brackets which does neither require Dirac’s formalism nor the symplectic method of Faddeev and Jackiw. This approach is based on the computation of the brackets between the constants of integration of the exact solutions of the equations of motion. From them all brackets of the dynamical variables of the system can be deduced in a straightforward way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

From the Weyl quantization of a particle on the circle to number–phase Wigner functions

A generalized Weyl quantization formalism for a particle on the circle is shown to supply an effective method for defining the number–phase Wigner function in quantum optics. A Wigner function for the state ϱ{sup ^} and the kernel K for a particle on the circle is defined and its properties are analysed. Then it is shown how this Wigner function can be easily modified to give the number–phase Wigner function in quantum optics. Some examples of such number–phase Wigner functions are considered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions

A detailed Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions is performed. We obtain for the theories under study the constraints, the gauge transformations, the generalized Faddeev–Jackiw brackets and we perform the counting of physical degrees of freedom. In addition, we compare our results with those found in the literature where the canonical analysis is developed, in particular, we show that both the generalized Faddeev–Jackiw brackets and Dirac’s brackets coincide to each other. Finally we discuss some remarks and prospects. - Highlights: • A detailed Faddeev–Jackiw analysis for exotic action of gravity is performed. • We show that Dirac’s brackets and Generalized [FJ] brackets are equivalent. • Without fixing the gauge exotic action is a non-commutative theory. • The fundamental gauge transformations of the theory are found. • Dirac and Faddeev–Jackiw approaches are compared.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization

We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Landau level quantization of Dirac electrons on the sphere

Interactions in Landau levels can stabilize new phases of matter, such as fractionally quantized Hall states. Numerical studies of these systems mostly require compact manifolds like the sphere or a torus. For massive dispersions, a formalism for the lowest Landau level on the sphere was introduced by Haldane (1983). Graphene and surfaces of 3D topological insulators, however, display massless (Dirac) dispersions, and hence require a different description. We generalize a formalism previously developed for Dirac electrons on the sphere in zero field to include the effect of an external, uniform magnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Transverse momentum structure of proton within the basis light-front quantization framework

We obtain the leading-twist valence quark transverse-momentum-dependent parton distribution functions (TMD PDFs) for the proton within the basis light-front quantization (BLFQ) framework. Our results are consistent with lattice QCD calculations and our previous results for the collinear limit. We also obtain consistency with the Soffer-type bounds. Within our approach, we find that six T-even TMDs in the leading twist are all independent of each other, and previously found model-dependent relations do not hold. This is a promising sign that our results are representative of future, more extensive treatments of QCD. Furthermore, we obtain a non-trivial x-dependence of the <(p ⊥ ) 2 > and some consistency with the Gaussian ansatz but only in the small <(p ⊥ ) 2 > region. Those features suggest our results may be a useful alternative in future experimental extractions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Nonperturbative Lorentz violation and field quantization

Regimes of Lorentz-violating effective field theories are studied in which departures from Lorentz symmetry are nonperturbative. Within a free toy theory exhibiting Lorentz breakdown involving an operator of mass dimension three, it is shown that conventional methods suffice to achieve field quantization and Fock-space construction. However, the absence of an observer-invariant energy-positivity condition requires physical input beyond the free theory for the unambiguous identification of a ground state. An investigation of the role of thermodynamics in this context is instigated.

Ground state↗
DOE OSTI2021

Size quantization of an exciton: A toy model of the “dead layer”

In this paper, size-quantization levels of an exciton in large nanocrystals is studied theoretically. For the nanocrystal size, L , much bigger than the Bohr radius, a B , the level positions do not depend on a B . The correction to the levels in a small parameter a B / L depends on the reflection phase of the exciton from the boundary. Calculation of this phase constitutes a three-body problem: electron, hole, and the boundary. This calculation can be performed analytically in the limit when the hole is much heavier than the electron. Physically, a slow motion of the hole towards the boundary takes place in the effective potential created by the fast motion of the electron orbiting the hole and touching the boundary. As a result, the hole is reflected before reaching the boundary. The distance of the closest approach of the hole to the boundary (the dead layer) exceeds a B parametrically .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Magic angle and height quantization in nanofacets on SiC(0001) surfaces

We report on the density-functional calculations that provide microscopic mechanism of the facet formation on the SiC (0001) surface. We first identify atom-scale structures of single-, double-, and quad-bilayer steps and find that the single-bilayer (SB) step has the lowest formation energy. We then find that the SB steps are bunched to form a nanofacet with a particular angle relative to the (0001) plane (magic facet angle) and with a discretized height along the (0001) direction (height quantization). We also clarify a microscopic reason for the self-organization of the nanofacet observed experimentally.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces

A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in the quantum theory, an according formalism for constrained variational discrete systems is constructed. While this paper focuses on global evolution moves and, for simplicity, restricts to flat configuration spaces R{sup N}, a Paper II [P. A. Höhn, “Quantization of systems with temporally varying discretization. II. Local evolution moves,” J. Math. Phys., e-print http://arxiv.org/abs/arXiv:1401.7731 [gr-qc].] discusses local evolution moves. In order to link the covariant and canonical picture, the dynamics of the quantum states is generated by propagators which satisfy the canonical constraints and are constructed using the action and group averaging projectors. This projector formalism offers a systematic method for tracing and regularizing divergences in the resulting state sums. Non-trivial coarse graining evolution moves lead to non-unitary, and thus irreversible, projections of physical Hilbert spaces and Dirac observables such that these concepts become evolution move dependent on temporally varying discretizations. The formalism is illustrated in a toy model mimicking a “creation from nothing.” Subtleties arising when applying such a formalism to quantum gravity models are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Quantization of a particle on a two-dimensional manifold of constant curvature

The formulation of quantum mechanics on spaces of constant curvature is studied. It is shown how a transition from a classical system to the quantum case can be accomplished by the quantization of the Noether momenta. These can be determined by means of Lie differentiation of the metric which defines the manifold. For the metric examined here, it is found that the resulting Schrödinger equation is separable and the spectrum and eigenfunctions can be investigated in detail.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Quantization of systems with temporally varying discretization. II. Local evolution moves

Several quantum gravity approaches and field theory on an evolving lattice involve a discretization changing dynamics generated by evolution moves. Local evolution moves in variational discrete systems (1) are a generalization of the Pachner evolution moves of simplicial gravity models, (2) update only a small subset of the dynamical data, (3) change the number of kinematical and physical degrees of freedom, and (4) generate a dynamical (or canonical) coarse graining or refining of the underlying discretization. To systematically explore such local moves and their implications in the quantum theory, this article suitably expands the quantum formalism for global evolution moves, constructed in Paper I [P. A. Höhn, “Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces,” J. Math. Phys. 55, 083508 (2014); e-print http://arxiv.org/abs/arXiv:1401.6062 [gr-qc]], by employing that global moves can be decomposed into sequences of local moves. This formalism is spelled out for systems with Euclidean configuration spaces. Various types of local moves, the different kinds of constraints generated by them, the constraint preservation, and possible divergences in resulting state sums are discussed. It is shown that non-trivial local coarse graining moves entail a non-unitary projection of (physical) Hilbert spaces and “fine grained” Dirac observables defined on them. Identities for undoing a local evolution move with its (time reversed) inverse are derived. Finally, the implications of these results for a Pachner move generated dynamics in simplicial quantum gravity models are commented on.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Quantization of interface currents

At the interface of two two-dimensional quantum systems, there may exist interface currents similar to edge currents in quantum Hall systems. It is proved that these interface currents are macroscopically quantized by an integer that is given by the difference of the Chern numbers of the two systems. It is also argued that at the interface between two time-reversal invariant systems with half-integer spin, one of which is trivial and the other non-trivial, there are dissipationless spin-polarized interface currents.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Quantization and anomalous structures in the conductance of Si/SiGe quantum point contacts

Quantum point contacts (QPCs) are fabricated on modulation-doped Si/SiGe heterostructures and ballistic transport is studied at low temperatures. We observe quantized conductance with subband separations up to 4 meV and anomalies in the first conductance plateau at 4e{sup 2}/h. At a temperature of T = 22 mK in the linear transport regime, a weak anomalous kink structure arises close to 0.5(4e{sup 2}/h), which develops into a distinct plateau-like structure as temperature is raised up to T = 4 K. Under magnetic field parallel to the wire up to B = 14 T, the anomaly evolves into the Zeeman spin-split level at 0.5(4e{sup 2}/h), resembling the '0.7 anomaly' in GaAs/AlGaAs QPCs. Additionally, a zero-bias anomaly (ZBA) is observed in nonlinear transport spectroscopy. At T = 22 mK, a parallel magnetic field splits the ZBA peak up into two peaks. At B = 0, elevated temperatures lead to similar splitting, which differs from the behavior of ZBAs in GaAs/AlGaAs QPCs. Under finite dc bias, the differential resistance exhibits additional plateaus approximately at 0.8(4e{sup 2}/h) and 0.2(4e{sup 2}/h) known as '0.85 anomaly' and '0.25 anomaly' in GaAs/AlGaAs QPCs. Unlike the first regular plateau at 4e{sup 2}/h, the 0.2(4e{sup 2}/h) plateau is insensitive to dc bias voltage up to at least V{sub DS} = 80 mV, in-plane magnetic fields up to B = 15 T, and to elevated temperatures up to T = 25 K. We interpret this effect as due to pinching off one of the reservoirs close to the QPC. We do not see any indication of lifting of the valley degeneracy in our samples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Torus as phase space: Weyl quantization, dequantization, and Wigner formalism

The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation for the dynamics of general quantum observables is written through the Moyal brackets on the torus and the support of the Wigner transform is characterized. Finally, a dequantization procedure is introduced that applies, for instance, to the Pauli matrices. As a result we obtain the corresponding classical symbols.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quantization effects in semiconductor nanostructures and singlet fission in molecular chromophores for photovoltaics and solar fuels

Hot carriers in semiconductors are electrons and/or holes that have energies greater than carriers that reside at the top and bottom of the conduction and valence bands, respectively; the latter carriers are in equilibrium with the lattice and have a temperature equal to the lattice (ambient) temperature. Hot carriers are created in semiconductors upon the absorption of photons with energies greater than the bandgap. The excess energy above the bandgap energy is in the form of kinetic energy. The hot carriers can cool to the lattice temperature via electron–phonon scattering and establish separate Boltzmann distributions for electrons and holes at the band edges. Thus, upon cooling, the excess kinetic energy of the hot carriers is transformed into heat and is unavailable to be converted into electrical or chemical free energy in a solar photon-converting cell. This hot-carrier cooling process significantly limits the maximum possible power conversion efficiency (PCE) of the free energy of solar photons into electrical free energy or chemical free energy in chemical bonds of fuels. However, if hot-carrier cooling can be slowed such that the hot carriers can be extracted before cooling to create higher photovoltages, or utilized to create additional electron-hole pairs through carrier multiplication, then beneficial use can be made of the excess energy of hot carriers and the maximum thermodynamic PCE can be dramatically increased. Quantization effects in semiconductor nanostructures, unique properties of some bulk semiconductors, and exciton multiplication in both semiconductors and molecular chromophores that undergo singlet fission have shown a path forward for potential dramatic increases in the PCEs of solar photons into electricity and solar fuels. The status, history, and future promise of the science and technology of these future approaches for different types of photovoltaic cells and cells for solar fuels will be discussed.

14 SOLAR ENERGY↗