General Symmetry Properties Research Articles

Carrollian approach to 1 + 3D flat holography

The isomorphism between the (extended) BMS4 algebra and the 1 + 2D Carrollian conformal algebra hints towards a co-dimension one formalism of flat holography with the field theory residing on the null-boundary of the asymptotically flat space-time enjoying a 1 + 2D Carrollian conformal symmetry. Motivated by this fact, we study the general symmetry properties of a source-less 1 + 2D Carrollian CFT, adopting a purely field-theoretic approach. After deriving the position-space Ward identities, we show how the 1 + 3D bulk super-translation and the super-rotation memory effects emerge from them, manifested by the presence of a temporal step-function factor in the same. Temporal-Fourier transforming these memory effect equations, we directly reach the bulk null-momentum-space leading and sub-leading soft graviton theorems. Along the way, we construct six Carrollian fields {S}_0^{pm } , {S}_1^{pm } , T and overline{T} corresponding to these soft graviton fields and the Celestial stress-tensors, purely in terms of the Carrollian stress-tensor components. The 2D Celestial shadow-relations and the null-state conditions arise as two natural byproducts of these constructions. We then show that those six fields consist of the modes that implement the super-rotations and a subset of the super-translations on the quantum fields. The temporal step-function allows us to relate the operator product expansions (OPEs) with the operator commutation relations via a complex contour integral prescription. We deduce that not all of those six fields can be taken together to form consistent OPEs. So choosing {S}_0^{+} , {S}_1^{+} and T as the local fields, we form their mutual OPEs using only the OPE-commutativity property, under two general assumptions. The symmetry algebra manifest in these holomorphic-sector OPEs is then shown to be Vir overset{wedge }{ltimes overline{textrm{sl}left(2,{mathbb{R}}right)}} with an abelian ideal.

Symmetry properties of a Brownian motor with a sawtooth potential perturbed by harmonic fluctuations

We present a study of general symmetry properties of a Brownian ratchet model. The study is based both on constructing chains of symmetry transformations reflecting explicit and hidden symmetries of the average ratchet velocity as a functional of the spatially periodic potential energy of a nanoparticle and on taking into account the symmetry types of periodic functions that are components of the potential energy of an additive-multiplicative form. A ratchet with a sawtooth stationary potential profile, dichotomously perturbed by a spatially harmonic signal, is investigated. Conclusions are made on both the possibility of occurrence of the ratchet effect and its direction for given values of the asymmetry parameter of the sawtooth profile, phase shifts of the control component, and frequencies of temporal fluctuations. These conclusions have been obtained only on the basis of symmetry transformations; that demonstrates the predictive value of the approach presented. The results of the symmetry analysis are confirmed by numerical simulation of the functioning of a ratchet with dichotomous stochastic spatially periodic fluctuations of the nanoparticle potential energy.

Space-time symmetry of brownian motors controlled by a dichotomous process

Studying the symmetry of different systems allows one to formulate a variety of conclusions regarding their properties without knowing the detailed information about a particular system. The models of Brownian motors (ratchets) relate the spatial-temporal dependence of the potential energy of Brownian particles and the resulting ratchet effect. In this article, we use the symmetry description of ratchet systems to study the mechanisms of the influence of the spatial and (or) temporal asymmetry of a nanosystem on the average velocity of Brownian motors of the two main types - with fluctuating periodic potential energy and fluctuating force (the so-called pulsating and forced (or tilted) ratchets). We consider the overdamped motion of a Brownian particle in an unbiased force field, which is described by a periodic stepwise coordinate function, that undergoes dichotomous changes with time. The use of symmetry transformations and symmetry properties of Brownian motors made it possible to obtain compact analytical representations of the average velocity of pulsating and forced ratchets as a function of the parameters of the spatial and temporal asymmetries of the force fields. The fundamental difference between the dependences of the average velocity of the Brownian motors of these two types on the asymmetry parameters is revealed. For the pulsating Brownian motors, the directed motion of nanoparticles is absent in a spatially symmetric system regardless of the presence of temporal asymmetry; the motion appears in the presence of spatial asymmetry, and it is possible to obtain the motor stopping points by tuning the temporal asymmetry parameter of the control process. For the forced Brownian motors, it is the temporal asymmetry that permits the ratchet effect in spatially symmetric systems. For this reason, stopping points as a result of competition of spatial and temporal asymmetries are easier to realize precisely for the motors with fluctuating forces (forced ratchets). The results presented in this article were obtained by analyzing only general symmetry properties, without involving hidden symmetries of ratchet systems, therefore the results are also valid for inertial dynamics.

Reflections on an old problem: That of preserving the logical forms and symmetry

This paper is devoted to analyze and discuss some of the new aspects about the preservation of the logical forms appearing in ordinary reasoning and fuzzy logic. Considering a Basic Fuzzy Algebra (BFA) as the basic formal model for representing imprecise predicates, several classical properties of logical forms which can be not valid depending on the representation of the logical connectives in a BFA are studied. Special emphasis is put on the general symmetry property, or its absence in some logical forms that, in some particular cases and in some sense, can become symmetrical as they are, for instance, the linguistic negation, the law of perfect repartition, or the additive law of measures. In any case, the difference between what is supposed in a mathematical model and what can be checked in the reality cannot be forgotten since any reality, and the study of the ordinary reasoning in natural language is a clear example of that, is but an ‘observed reality’. Anyway, if what is in a mathematical fuzzy model is not always symmetrical, and since these models represent linguistic statements affected by imprecision and uncertainty, it can be concluded that, in general, neither plain language, nor commonsense or ordinary reasoning, show the same level of symmetry exhibited by the specialized language and the deductive reasoning allowing mathematical proofs.

Asymptotic neutron scattering laws for anomalously diffusing quantum particles.

The paper deals with a model-free approach to the analysis of quasielastic neutron scattering intensities from anomalously diffusing quantum particles. All quantities are inferred from the asymptotic form of their time-dependent mean square displacements which grow ∝t(α), with 0 ≤ α < 2. Confined diffusion (α = 0) is here explicitly included. We discuss in particular the intermediate scattering function for long times and the Fourier spectrum of the velocity autocorrelation function for small frequencies. Quantum effects enter in both cases through the general symmetry properties of quantum time correlation functions. It is shown that the fractional diffusion constant can be expressed by a Green-Kubo type relation involving the real part of the velocity autocorrelation function. The theory is exact in the diffusive regime and at moderate momentum transfers.

Spectral Band Replication (SBR) compression technology: Survey of the unified efficient low-cost implementations of complex exponential- and cosine-modulated QMF banks

Spectral Band Replication (SBR) is an enhancement compression technology, a bandwidth extension method which significantly improves the compression efficiency of perceptual audio and speech coding schemes. There are two versions of the SBR technology: Standard SBR and low delay SBR (LD-SBR). Central to the operation of standard and LD-SBR are dedicated complex exponential-modulated and real-valued cosine-modulated quadrature mirror filter (QMF) banks as the basic mathematical tools to analyze and synthesize audio signals. This tutorial paper presents the complete unified efficient implementations of complex exponential-modulated and real-valued cosine-modulated QMF banks used both in the standard SBR and LD-SBR encoder and decoder. In general, for each QMF bank is presented: Definition of its equivalent block transform with a common parameter M representing the number of sub-bands, its general symmetry property in the frequency or time domain, and the derivation of a fast algorithm for its efficient implementation. All fast algorithms are analyzed in detail in terms of the arithmetic complexity, regularity and structural simplicity for a potential real-time low-cost implementation in hardware or software.

General symmetry properties of incommensurately modulated crystals described by projective representations of line groups

After a detailed investigation of some fundamental general orthogonal symmetry properties of incommensurate condensed systems, the line groups are applied for describing the structure of such modulated crystals. It is demonstrated, that use of projective representations of these groups may give a more refined description of such structures and significantly extends applicability of the diffuse scattering formalism.

Plasmons localized at nanoscale perturbations of flat metal surface

We study the properties of plasmonic excitations localized at 2D and 3D nanoscale perturbations of a flat metal surface within the general method of surface integral equations. The resonant values of the optical permittivity &#x3B5;j and the plasmonic eigenfunctions&#x2014;distributions of the surface charge density &#x3C3;j(r)&#x2014;are investigated. General symmetry properties linking the cases of convex and concave perturbations (bumps and mirror-reflected pits) are established. The impact of the height-to-width perturbation ratio h0/r0 on the localized surface plasmons is twofold: while the resonant permittivities &#x3B5;j drop linearly with h0/r0 leading to strong redshifts of the resonances, the scale of localization stays constant (&#x2248;r0). The presence of sharp shape features (tips and corners) with the curvature radius &#x3C1;0&#x226A;r0 leads to superlocalization of charge density on the scale of &#x3C1;0 and, simultaneously, to an additional strong drop of &#x3B5;j.

Lattice density functional theory of the single-impurity Anderson model: Development and applications

A lattice density functional theory (LDFT) of the single-impurity Anderson model is presented. In this approach the basic variable is the single-particle density matrix ${\ensuremath{\gamma}}_{\mathit{ij}}$ with respect to the lattice sites and the fundamental unknown functional is the Coulomb interaction energy $W[\ensuremath{\gamma}]$. Using general symmetry properties, a two-level ansatz for $W[\ensuremath{\gamma}]$ in spin-restricted systems is proposed which involves explicitly only the impurity orbital and a single symmetry-adapted conduction-band state. A simple analytical functional dependence of $W[\ensuremath{\gamma}]$ is derived on the basis of exact results of this two-level problem. The resulting approximation is shown to be exact in two important opposite limits: a totally degenerate conduction band and a conduction band with widely separated discrete levels. Applications to finite rings having $N\ensuremath{\leqslant}100$ atoms yield very accurate results for ground-state properties such as the kinetic, interaction, and total energy, as well as the occupation and magnetic moment of the local impurity orbital. This holds for all considered interaction strengths, from weak to strong correlations, as well as in the Kondo and intermediate valence regimes. One concludes that the present two-level approximation provides an appropriate framework for investigating subtle electron-correlation effects of the Anderson model within LDFT.

A minimal inflation scenario

We elaborate on a minimal inflation scenario based entirely on the general propertiesof supersymmetry breaking in supergravity models. We identify the inflaton as the scalar component of the Goldstino superfield. We write plausible candidates for the effective action describing this chiral superfield. In particular the theory depends (apart from parameters of O(1)) on a single free parameter: the scale of supersymmetry breaking. This can be fixed using the amplitude of CMB cosmological perturbations and we therefore obtain the scale of supersymmetry breaking to be 1012−14 GeV. The model also incorporates explicit R-symmetry breaking in order to satisfy the slow roll conditions. In our model the η−problem is solved without extra fine-tuning. We try to obtain as much information as possible in a model independent way using general symmetry properties of the theory's effective action, this leads to a new proposal on how to exit the inflationary phase and reheat the Universe.

Molecular Symmetry Properties of Conical Intersections and Nonadiabatic Coupling Terms: Theory and Quantum Chemical Demonstration for Cyclopenta-2,4-dienimine (C5H4NH)

This paper discovers molecular symmetry (MS) properties of conical intersections (CIs) and the related nonadiabatic coupling terms (NACTs) in molecules which allow large amplitude motions such as torsion, in the frame of the relevant molecular symmetry group, focusing on groups with one-dimensional (1-d) irreducible representations (IREPs). If one employs corresponding MS-adapted nuclear coordinates, the NACTs can be classified according to those IREPs. The assignment is supported by theorems which relate the IREPs of different NACTs to each other, and by properties of the NACTs related to the CIs. For example, planar contour integrals of the NACTs evaluated along loops around the individual CIs are equal to +pi or -pi, depending on the IREP-adapted signs of the NACTs. The + or - signs for the contour integrals may also be used to define the "charges" and IREPs of the CIs. We derive various general molecular symmetry properties of the related NACTs and CIs. These provide useful applications; e.g., the discovery of an individual CI allows one to generate, by means of all molecular symmetry operations, the complete set of CIs at different symmetry-related locations. Also, we show that the seams of CIs with different IREPs may have different topologies in a specific plane of MS-adapted coordinates. Moreover, the IREPs impose symmetrical nodes of the NACTs, and this may support their calculations by quantum chemical ab initio methods, even far away from the CIs. The general approach is demonstrated by application to an example. Specifically, we investigate the CIs and NACTs of cyclopenta-2,4-dienimine (C(5)H(4)NH) which has C(2v)(M) molecular symmetry with 1-d IREPs. The results are confirmed by quantum chemical calculations, starting from the location of a CI based on the Longuet-Higgins phase change theorem, until a proof of self-consistency, i.e., the related symmetry-adapted NACTs fulfill quantization rules which have been derived in [Baer, M. Beyond Born-Oppenheimer: Electronic non-Adiabatic Coupling Terms and Conical Intersections; Wiley & Sons Inc.: Hoboken, NJ, 2006].

Fast computational structures for an efficient implementation of the complete TDAC analysis/synthesis MDCT/MDST filter banks

A new fast computational structure identical both for the forward and backward modified discrete cosine/sine transform (MDCT/MDST) computation is described. It is the result of a systematic construction of a fast algorithm for an efficient implementation of the complete time domain aliasing cancellation (TDAC) analysis/synthesis MDCT/MDST filter banks. It is shown that the same computational structure can be used both for the encoder and the decoder, thus significantly reducing design time and resources. The corresponding generalized signal flow graph is regular and defines new sparse matrix factorizations of the discrete cosine transform of type IV (DCT-IV) and MDCT/MDST matrices. The identical fast MDCT computational structure provides an efficient implementation of the MDCT in MPEG layer III (MP3) audio coding and the Dolby Labs AC-3 codec. All steps to derive the computational structure are described in detail, and to put them into perspective a comprehensive list of references classified into categories is provided covering new research results achieved in the time period 1999–2008 in theoretical and practical developments of TDAC analysis/synthesis MDCT/MDST filter banks (general mathematical, symmetry and special properties, fast MDCT/MDST algorithms and efficient software/hardware implementations of the MDCT in MP3).

Model independent analysis of polarization effects in elastic electron–deuteron scattering in presence of two-photon exchange

The general spin structure of the matrix element, for the elastic electron (positron)–deuteron scattering is parametrized using general symmetry properties of the hadron electromagnetic interaction, such as P-, C- and T-invariances as well as lepton helicity conservation in QED at high energy, taking into account the two-photon exchange contribution. The expressions for the differential cross section and for all polarization observables are given in terms of fifteen real functions. In presence of two photon exchange, deuteron electromagnetic form factors can still be extracted from electron and positron elastic scattering in the same kinematical conditions.

General theory of electromagnetic fluctuations near a homogeneous surface in terms of its reflection amplitudes

We derive general expressions for the fluctuating electromagnetic field outside a homogeneous material surface. The analysis is based on general results from the thermodynamics of irreversible processes, and requires no consideration of the material interior, as it only uses knowledge of the reflection amplitudes for its surface. Therefore, our results are valid for all homogeneous surfaces, including layered systems and metamaterials, at all temperatures. In particular, we obtain formulas for the near-field region, which are important for interpreting the numerous current experiments probing proximity effects for macroscopic and/or microscopic bodies separated by small empty gaps. By use of Onsager's reciprocity relations, we obtain also the general symmetry properties that must be satisfied by the reflection matrix of any material.

Kondo effect in asymmetric Josephson couplings through a quantum dot

Asymmetry in the Josephson couplings between two superconductors through a quantum dot is studied based on a single impurity Anderson model using the numerical renormalization group (NRG). Specifically, we examine how the difference between the couplings ΓL and ΓR affects the ground state, which is known to show a quantum phase transition between a nonmagnetic singlet and a magnetic doublet depending on the various parameters; the Coulomb interaction U, onsite potential , level width caused by the hybridization, and superconducting (SC) gap for the leads on the left and right (). Our results show that whether the local moment is fully screened or not depends substantially on the asymmetry in the couplings . It tends to make the singlet ground state stable, while the amplitude and phase difference of the SC gaps tend to suppress the screening. We also discuss some general symmetry properties of the system and their relation to the current conservation.

Symmetry preserving optimised effective potential theory (application to atoms)

In this paper, general symmetry properties of physical systems are used in order to produce a mapping of the external potential of a many electron system to its optimized effective potential (OEP). The so derived effective potential is used to calculate the OEP ground state energies and spin orbitals. Applications are made to atoms and ions and the results are compared to those of the exact Hartree-Fock approximation. The relative deviations from the exact HF theory (△E/E) are of the order of 10−4. The same holds for molecules. One of the features of the present theory is that the many electron wave functions derived by the present method, transform according to the irreducible representations of the exact states.

An exact two-dimensional model for a periodic circular array of head-to-head permanent magnets

An analytical expression is derived for the magnetic field of a two-dimensional periodic circular array of head-to-head permanent magnets, assuming there is either no gap between the magnets or that they are separated by a non-magnetic pole-piece. Some more general symmetry properties are described. The force experienced by the magnets is calculated and an analytical approximation is derived. We comment on the published dipole-approximation used for dealing with this kind of problem and also correct some mistakes.

Magneto-Electro-Optical Properties of the Quantum Vacuum and Lorentz Invariance

We consider the magneto-electric optical properties of the quantum vacuum and show that all the different phenomenona are related by Lorentz invariance. As a model calculation we show how crossed fields properties can be calculated starting from single field properties by using Lorentz transformations. Using this method we have studied for the first time the case of a crossed static magnetic field and electric field applied with one of these two fields parallel to the direction of light propagation. We also show that parallel field properties can be found using general symmetry properties.

Order parameter in superconductors with nondegenerate bands

In noncentrosymmetric metals, the spin degeneracy of the electronic bands is lifted by spin-orbit coupling. We consider general symmetry properties of the pairing function Delta(k) in noncentrosymmetric superconductors with spin-orbit coupling (NSC), including CePt3Si, UIr and Cd2Re2O7. We find that Delta(k) = chi(k) t(k), where chi(k) is an even function which transforms according to the irreducible representations of the crystallographic point group and t(k) is a model dependent phase factor. We consider tunnelling between a NSC and a conventional superconductor. It is found that, in terms of thermodynamical properties as well as the Josephson effect, the state of NSC resembles a singlet superconducting state with gap function chi(k).

High-energy above-threshold detachment from negative ions

Above-threshold detachment of electrons from negative ions by an elliptically polarized laser field is analyzed within the strong-field approximation. The low-energy part of the spectrum, that is, its structure and its apparent cutoff, strongly depends on the orbital quantum number $l$ of the initial ground state. The high-energy part is characterized by the usual extended plateau caused by rescattering, which is essentially independent of the ground state. The potential that the returning electron experiences during rescattering is modeled by the sum of a polarization potential and a static potential. This rescattering potential does not have much effect on the shape of the plateau, but it does on its height. For ${\mathrm{H}}^{\ensuremath{-}}\phantom{\rule{0.2em}{0ex}}(l=0)$, the yield of rescattered electrons is five orders of magnitude below the direct electrons, while for ${\mathrm{I}}^{\ensuremath{-}}\phantom{\rule{0.2em}{0ex}}(l=1)$ the yields only differ by a factor of 40. We also analyze the dependence of the angle-resolved energy spectrum on the ellipticity of the laser field and confirm general symmetry properties. An angle-integrated elliptic dichroism parameter is introduced and analyzed.