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With the rapid development in sensor network technology, the complexity and diversity of application scenarios have put forward more and more new requirements for inductor–capacitor (LC) sensors, for instance, multi-parameter simultaneous monitoring. Here, the parity–time (PT) symmetry concept in quantum mechanics is applied to LC passive wireless sensing. Two or even three parameters can be monitored simultaneously by observing the frequency response of the reflection coefficient at the end of the readout circuit. In particular, for three-parameter detection, a novel detection method is studied to extract the three resonant frequencies of the system through the phase–frequency characteristics of the reflection coefficient, which has never appeared in the previous literature on PT symmetry. The changes in three resonant frequencies are in response to changes in the three parameters in the environment. We show theoretically and demonstrate experimentally that the PT-symmetric LC sensor can realize multi-parameter measurement using a series LCR circuit as the sensor and a symmetric adjustable LCR circuit as the readout circuit. Our work paves the way for applying PT symmetry in multi-parameter detection. [ABSTRACT FROM AUTHOR]

Using a high-precision code, we generate the eigenstates of a PT-symmetric Hamiltonian. We solve the time-dependent Schrödinger equation (TDSE) of the non-Hermitian system based on the eigenset. Since the formulation is relatively new and the observables are calculated differently than conventional quantum mechanics, we justify it with a paradigmatic case in Hermitian quantum mechanics. We present the harmonic generation spectra on some model PT-Hamiltonians driven by an electric pulse. We discuss the physical differences with the harmonic spectra of a pulse-driven atom. [ABSTRACT FROM AUTHOR]

In this article, we study the log-log blowup dynamics for the mass critical nonlinear Schrödinger equation on R² under rough but structured random perturbations at L².R²/ regularity. In particular, by employing probabilistic methods, we provide a construction of a family of L².R²/ regularity solutions which do not lie in Hs.R²/ for any s > 0, and which blowup according to the log-log dynamics. [ABSTRACT FROM AUTHOR]

Using the Lie classical method, the potential symmetry of the generalized hyperbolic quasilinear and Boussinesq equations is investigated. To find these symmetries in specific cases, we study various scientific examples that admit these symmetries. In addition, using this method, the potential symmetries of the conservative forms of the Boussinesq equation is determined. [ABSTRACT FROM AUTHOR]

In this paper, the modified Dirac equation (MDE) has been solved approximately for improved Manning–Rosen plus quasi-Hellman potentials (IMRQHPs), including the improved Yukawa tensor interaction under new spin symmetry and pseudospin symmetry for arbitrary spin–orbit number k , an appropriate approximation employed on the centrifugal terms in the symmetries of three-dimensional extended relativistic quantum mechanics (3D-ERQM). This potential is a superposition of Manning–Rosen plus quasi-Hellman potentials and some other exponential terms. Through the application of both new approximations to deal with the centrifugal term, Bopp's shift method and the independent-time perturbation theory method, the recent modified approximate energy corrections under IMRQHPs are obtained for nuclei 1 7 O and 1 7 F and (O2, I2, N2, H2, LiH, CO and NO) diatomic molecules in 3D-ERQM and three-dimensional extended non-relativistic quantum mechanics (3D-ENRQM) symmetries. The recent values that we get appear sensitive to (j , k , l ∕ l ̃ , s ∕ s ̃ , m ∕ m ̃) , which are known as the discrete atomic quantum numbers, the mixed potential depths (C ∕ A , D ∕ B) and (V 0 ∕ a , V 1 ∕ b) , the range of the potential α and non-commutativity parameters (Θ , σ , χ). In both 3D-ERQM and 3D-ENRQM symmetries, we show that the recent corrections obtained on the new bound states under IMRQHPs are infinitesimal to the principal part of energy in the ordinary cases of 3D-RQM and 3D-NRQM symmetries. In the new symmetries of 3D-ERQM symmetries, it is not possible to get the exact analytical solutions k = 1 and k ≠ − 1 , only the approximate solutions are possible. In addition, we discussed in detail the non-relativistic study of the studied mixed potentials. Four special cases, i.e. we investigated some special cases in the context of modified Schrödinger theories. In the framework of known relativistic quantum mechanics, we have clearly demonstrated that the modified Schrödinger equation can be represented as the Dirac equation under the influence of IMRQHPs. [ABSTRACT FROM AUTHOR]

Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of Galilean transformations. In quantum mechanics, Galilean boosts require a non-trivial transformation rule for the wave function and a concomitant "projective representation" of the Galilean symmetry group. Using Feynman's path integral formalism, this latter result can be shown to be equivalent to the non-invariance of the Lagrangian. Thus, using path integral methods, the representation of certain symmetry groups in quantum mechanics can be simply understood in terms of the transformation properties of the classical Lagrangian and conversely. The main results reported here should be accessible to students and teachers of physics—particularly classical mechanics, quantum mechanics, and mathematical physics—at the advanced undergraduate and beginning graduate levels, providing a useful exposition for those wanting to explore topics such as the path integral formalism for quantum mechanics, relativity principles, Lagrangian mechanics, and representations of symmetries in classical and quantum mechanics. [ABSTRACT FROM AUTHOR]

A quantum symmetry called entanglement-assisted invariance, also called envariance, is introduced. It is studied with respect to the process of performing quantum measurements. An apparatus which interacts with other physical systems, which are called environments, exchanges a single state with physical states equal in number to that of the possible outcomes of the experiment. Correlations between the apparatus and environment give rise to a type of selection rule which prohibits the apparatus from appearing in a superposition corresponding to different eigenvalues of the pointer basis of the apparatus. The eigenspaces of this observable form a natural basis for the apparatus and determine the observable of the measured quantum system. It is also discussed how statistical mechanics can be formulated in terms of this symmetry. [ABSTRACT FROM AUTHOR]

A path-integral approach is used to study the spectral properties of the generators of the SO(2, 1) symmetry of conformal quantum mechanics (CQM). In particular, we consider the CQM version that corresponds to the weak-coupling regime of the inverse square potential. We develop a general framework to characterize a generic symmetry generator G (linear combinations of the Hamiltonian H, special conformal operator K, and dilation operator D), from which the path-integral propagators follow, leading to a complete spectral decomposition. This is done for the three classes of operators: Elliptic, parabolic, and hyperbolic. We also highlight novel results for the hyperbolic operators, with a continuous spectrum, and their quantum-mechanical interpretation. The spectral technique developed for the eigensystem of continuous-spectrum operators can be generalized to other operator problems. [ABSTRACT FROM AUTHOR]

It has been recently argued that by Leifer and Pusey, and Price, that time-symmetric quantum mechanics must entail retrocausality. Adlam responds that such theories might also entail 'spooky action at a distance'. This paper proposes a third alternative: time-symmetric quantum mechanics might entail temporal global correlations. Unlike the traditional analysis of time symmetries in quantum mechanics, which consider linear and unitary interpretations, this paper considers the time-symmetric collapse models advanced by Bedingham and Maroney. These models are specially interesting since it has been widely believed that collapse theories cannot be time-reversal invariant. [ABSTRACT FROM AUTHOR]

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Relativistic and nonrelativistic quantum mechanics formulated in a noncommutative space-space have recently become the object of renewed interest. In the context of extended relativistic quantum mechanics (ERQM) symmetries with arbitrary spin-orbit coupling quantum number k , we approximate to solve the deformed Dirac equation (DDE) for a new suggested new generalized Schiöberg and Manning–Rosen potentials within the generalized (Coulomb and Yukawa)-like tensor interactions (NGSM-GLTs). In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the global new energy eigenvalue which equals the energy eigenvalue in usual relativistic quantum mechanics (RQM) as the main part plus three corrected parts produced from the effect of the spin-orbit interaction, the new modified Zeeman, and the rotational Fermi term, by using the parametric of the well-known Bopp's shift method and standard perturbation theory using Greene–Aldrich approximation to handle 1 / r , 1 / r 2 and other terms in the effective potential. The new values that we got appeared sensitive to the quantum numbers (j , k , l / l ̃ , s / s ̃ , m / m ̃), the mixed potential depths ( D 0 , D 1 , σ , α , A), the range of the potential δ , and noncommutativity parameters (Θ , τ , χ). We recovered several potentials, including the improved Schiöberg and Manning–Rosen potentials within the improved Yukawa-like tensor interaction, the new Schiöberg and Manning–Rosen potentials within the improved Coulomb-like tensor interaction, the new Schiöberg potential within the improved Yukawa-like tensor interaction, the new Manning–Rosen potential within the improved Yukawa-like tensor interaction, and the new Schiöberg and Manning–Rosen potentials potential problems in the context of nonrelativistic extended quantum mechanics symmetries. [ABSTRACT FROM AUTHOR]

The analytical solutions of the mass-dependent Klien-Gordon equation (KGE) with the improved harmonic oscillator potential and the improved vector quark-antiquark interaction are derived from the symmetries of three-dimensional relativistic noncommutative quantum mechanics (3D-RNCQM symmetries) using Bopp's shift method and perturbation theory. The energy state equations are sensitive to the global parameters characterizing the noncommutativity space-space (Θ, σ) and the potential parameter (Enl, a, b, c, m0, k) in addition to the discrete atomic quantum numbers (j,l,s,m). The energy spectra for the mass-dependent Shrödinger equation with improved vector quark-antiquark interaction and harmonic oscillator potential were found using nonrelativistic limit principles. We also used the current findings to determine the heavy-meson masses of charmonium cc and bottomonium bb; in both ordinary nonrelativistic quantum mechanics symmetries and three-dimensional nonrelativistic noncommutative 3D-NRNCQM symmetries. [ABSTRACT FROM AUTHOR]

It has been argued that measurement-induced collapses in Orthodox Quantum Mechanics generates an intrinsic (or built-in) quantum arrow of time. In this paper, I critically assess this proposal. I begin by distinguishing between an intrinsic and non-intrinsic arrow of time. After presenting the proposal of a collapse-based arrow of time in some detail, I argue, first, that any quantum arrow of time in Orthodox Quantum Mechanics is non-intrinsic since it depends on external information about the measurement context, and second, that it cannot be global, but just local. I complement these arguments by assessing some criticisms and considerations about the implementation of time reversal in contexts wherein measurement-induced collapses work. I conclude that the quantum arrow of time delivered by Orthodox Quantum Mechanics is much weaker than usually thought. [ABSTRACT FROM AUTHOR]

In this work, the bound state solutions of the deformed Dirac equation (DDE) have been determined with the improved generalized inversely quadratic Yukawa potential including Coulomb-like tensor (IGIQYPCLT) interaction under the condition of spin symmetry and pseudospin symmetry in the deformation Dirac theory (DDT) symmetries for with the arbitrary spin-orbit quantum number k. The IGIQYPCLT interaction includes generalized inversely quadratic Yukawa potential as the main part and other new exponential terms due to the topological properties of deformation space space. The parametric Bopp's shift method and standard perturbation theory are used to obtain the relativistic and nonrelativistic energy eigenvalues for studied potential. The new values that we get appeared sensitive to the quantum numbers j , k , l , l ~ , s , s ~ , m , m ~ , the mixed potential depths V 0 , T , the range of the potential α , and noncommutativity parameters Θ , σ , χ . The energies spectra of the improved Mie-type potential within improved Coulomb-like potential within improved have been derived as particular cases of the IGIQYPCLT model. We have applied our results to obtaining the new nonrelativistic energies that represent the binding energy between the quark and anti-quark to determine the modified spin-averaged mass spectra of heavy and heavy-light mesons HLM such as c c ¯ , b b ¯ , b c ¯ , b s ¯ , c s ¯ , and b q ¯ , q = (u, d) in both NRQM and ENRQM symmetries. It is worth mentioning that, for all cases, to make the three simultaneous limits Θ , σ , χ → 0 , 0 , 0 , the ordinary physical quantities are recovered all known physical values in the framework of relativistic and nonrelativistic quantum mechanics known in the literature. [ABSTRACT FROM AUTHOR]

The conservation of information of evaporating black holes is a very natural consequence of unitarity, which is the fundamental symmetry of quantum mechanics. In order to study the conservation of information, we need to understand the nature of the entanglement entropy. The entropy of Hawking radiation is approximately equal to the maximum of entanglement entropy if a black hole is in a state before the Page time, i.e., when the entropy of Hawking radiation is smaller than the entropy of the black hole. However, if there exists a process generating smaller entanglements rather than maximal entanglements, the entropy of Hawking radiation will become smaller than the maximum of the entanglement entropy before the Page time. If this process accumulates, even though the probability is small, the emitted radiation can eventually be distinguished from the exactly thermal state. In this paper, we provide several interpretations of this phenomenon: (1) information of the collapsed matter emitted before the Page time, (2) there exists a firewall or a non-local effect before the Page time, or (3) the statistical entropy is greater than the areal entropy; a monster is formed. Our conclusion will help resolve the information loss paradox by providing groundwork for further research. [ABSTRACT FROM AUTHOR]

The article titled "Envariance as a Symmetry in Quantum Mechanics and Applications to Statistical Mechanics" has been retracted by the Symmetry Editorial Office. Concerns were raised about the article's overlap with previously published studies by different authors. An investigation confirmed that sections 2-5 of the article contained text and equations that were not appropriately acknowledged or cited from the earlier studies. As a result, the article has been retracted in accordance with MDPI's retraction policy and the Committee on Publication Ethics's retraction guidelines. The authors did not provide a comment on this decision. [Extracted from the article]

In this work, we considered analytical approximate bound state solutions of the mass-dependent deformed Dirac equation with the improved vector Eckart potential including the Yukawa tensor interaction (IEPDMYI for short) in the context of extended relativistic quantum mechanics ERQM symmetries. The new relativistic energy spectra of the DDE for the IEPDMYI with spin symmetry and pseudospin symmetry are obtained. The solutions for arbitrary k-wave are obtained by using the basic concept of Bopp's shift approach and standard perturbation by applying an approximation to the centrifugal-like term in the calculations. The new values that we get appeared sensitive to the discrete quantum numbers (j , k , l , l ̃ , s , s ̃ , m , m ̃) , the mixed potential depths (V 1 , V 2 , V 0) , the range of the potential α and noncommutativity parameters (Θ , σ , χ). We have highlighted three physical phenomena that automatically generate a result of the topological properties of noncommutativity, the first physical phenomena are the perturbative spin-orbit coupling, the second is the magnetic induction while the third corresponds to the rotational proper phenomena. We show that the corrections on the spectrum energy are smaller than the main energy in the usual cases of quantum field theory. In the ERQM symmetries, it is not possible to get the exact analytical solutions for (k = 0 , − 1 , + 1) , only the approximate solutions are available. We have obtained the energy equation for several well-known potentials by choosing appropriate parameters in the improved Eckart potential model such as the improved Hulthén potential and the improved generalized Morse potential. [ABSTRACT FROM AUTHOR]

We approximately solve the deformed Dirac equation for a new improved Hulthén plus a class of Yukawa potential including a Coulomb-like tensor interaction (IHCYPCTI for short) in the context of extended relativistic quantum mechanics ERQM symmetries including an improved Coulomb-like tensor interaction with an arbitrary spin-orbit coupling quantum number k. Within the framework of the spin and pseudospin (p-spin) symmetry, we obtain the global new energy eigenvalue which equals the energy eigenvalue in usual relativistic QM plus the corrected energy induced by three infinitesimal additive parts of the Hamiltonian corresponding to the spin-orbit interaction, the new modified Zeeman and the rotational Fermi term by using the parametric of Bopp's shift method and standard perturbation theory with an approximation to the centrifugal term. The new values that we got appeared sensitive to the quantum numbers (j, k, l,Ĩ, s, ..., m, ...), the mixed potential depths (A, B), the range of the potential δ, and noncommutativity parameters (Θ, σ, χ). The mixed potential which in some particular cases gives solutions of different potentials: the improved Hulthén, the improved Yukawa potential and the improved Coulomb-like problem along with their bound state energies are obtained. [ABSTRACT FROM AUTHOR]

The quantum interference between the decays of entangled neutral kaons is studied in the process ϕ → KSKL → π+π−π+π−, which exhibits the characteristic Einstein-Podolsky-Rosen correlations that prevent both kaons to decay into π+π− at the same time. This constitutes a very powerful tool for testing at the utmost precision the quantum coherence of the entangled kaon pair state, and to search for tiny decoherence and CPT violation effects, which may be justified in a quantum gravity framework. The analysed data sample was collected with the KLOE detector at DAΦNE, the Frascati ϕ-factory, and corresponds to an integrated luminosity of about 1.7 fb−1, i.e. to about 1.7 × 109ϕ → KSKL decays produced. From the fit of the observed ∆t distribution, being ∆t the difference of the kaon decay times, the decoherence and CPT violation parameters of various phenomenological models are measured with a largely improved accuracy with respect to previous analyses. The results are consistent with no deviation from quantum mechanics and CPT symmetry, while for some parameters the precision reaches the interesting level at which — in the most optimistic scenarios — quantum gravity effects might show up. They provide the most stringent limits up to date on the considered models. [ABSTRACT FROM AUTHOR]

We employed the elegant tool of Bopp's shift and standard perturbation theory methods to obtain a new relativistic and nonrelativistic approximate bound state solution of deformed Klein–Gordon DKG and deformed Schrödinger DSE equations using the modified equal vector scalar Manning–Rosen plus quadratic Yukawa potential (MVSMQY-Ps) model. Furthermore, we have employed the improved approximation to the centrifugal term for some selected diatomic molecules such as N2, I2, HCl, CH and LiH in the symmetries of extended quantum mechanics to obtain the approximate solutions. The relativistic shift energy Δ E r m q y tot (n , δ , η , b , A , V 0 ′ , Θ , σ , χ , j , l , s , m) and the perturbative nonrelativistic corrections Δ E m q y n r (n , δ , η , b , A , V 0 ′ , Θ , σ , χ , j , l , s , m) appeared as a function of the parameters (δ , η , b , A , V 0 ′ ), the parameters of noncommutativity (Θ , σ , χ), in addition to the atomic quantum numbers (n , j , l , s , m). In both relativistic and nonrelativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM. A straightforward limit of our results to ordinary quantum mechanics shows that the present result under MVSMQAY-Ps is consistent with what is obtained in the literature. In the new symmetries of NCQM, it is not possible to get the exact analytical solutions for l = 0 and l ≠ 0 , and can only be solved approximately. We have observed that the DKGE under the MVSMQY-Ps model has a physical behavior similar to the Duffin–Kemmer equation for meson with spin-1; it can describe a dynamic state of a particle with spin-1 in the symmetries of RNCQM. Moreover, we have treated composite systems such as molecules made of N = 2 particles of masses m n (n = 1 , 2) in the frame of noncommutative algebra. The NRNCQM and RNCQM results obtained within Bopp's shift and standard perturbation theory methods overlap entirely with the results obtained by ordinary NCQM, and it displays that the theoretical investigation in this study is excellent. [ABSTRACT FROM AUTHOR]

We argue that Roberts's argument for the thesis that absolute velocity is not measurable in a Newtonian world is unsound, because it depends on an analysis of measurement that is not extensionally adequate. We propose an alternative analysis of measurement, one that is extensionally adequate and entails that absolute velocity is measured in at least one Newtonian world. If our analysis is correct, then this Newtonian world is a counterexample to the widely endorsed thesis that if a property varies under the symmetries of a theory then, according to that theory, the property could not be measured. Thus, our paper shows that the debate over the measurability of symmetry-variant properties is more unsettled than previously supposed. [ABSTRACT FROM AUTHOR]

In this work, we employed the elegant tool of Bopp's shift and standard perturbation theory methods to obtain a new relativistic and nonrelativistic approximate bound state solution of the deformed Klein-Gordon and deformed Schrödinger equations using the modified equal vector scalar Manning-Rosen plus a class of Yukawa potentials (DVSMCY-Ps, in short) model. Furthermore, we have employed the improved approximation to the centrifugal term for some selected diatomic molecules, such as N2, I2, HCl, CH, LiH, and CO, in the symmetries of extended quantum mechanics to obtain the approximate solutions. The relativistic shift energy Δ Etotmcy ( n,δ,η,b,A,V0,V0',Θ,σ,χ,j,l,s,m) and the perturbative nonrelativistic corrections Δ Enr mcy ( n,δ,η,b,A,V0,V0',Θ,σ,χ,j,l,s,m) appeared as a function of the parameters ( δ,η,b,A,V0,V0'), the parameters of noncommutativity ( Θ,σ,χ ), in addition to the atomic quantum numbers ( n,j,l,s,m). In both relativistic and nonrelativistic problems, we show that the corrections to the spectrum energy are smaller than the main energy in the ordinary cases of relativistic quantum mechanics and nonrelativistic quantum mechanics. A straightforward limit of our results to ordinary quantum mechanics shows that the present result under DVSMCY-Ps is consistent with what is obtained in the literature. In the new symmetries of noncommutative quantum mechanics, it is not possible to get exact analytical solutions for l=0, and l≠0 can only be solved approximately. We have observed that the DKGE under the DVSMCY-Ps model has a physical behavior similar to the Duffin-Kemmer equation for meson with spin-1, it can describe a dynamic state of a particle with spin-1 in the symmetries of relativistic noncommutative quantume mechanics. [ABSTRACT FROM AUTHOR]

Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced. It is shown that, given a groupoid G ⇉ Ω associated with a (quantum) system, there are two possible descriptions of its symmetries, one "microscopic", the other one "global". The microscopic point of view leads to the introduction of an additional layer over the grupoid G, giving rise to a suitable algebraic structure of 2-groupoid. On the other hand, taking advantage of the notion of group of bisections of a given groupoid, the global perspective allows to construct a group of symmetries out of a 2-groupoid. The latter notion allows to introduce an analog of the Wigner's theorem for quantum symmetries in the groupoid approach to Quantum Mechanics. [ABSTRACT FROM AUTHOR]

The broadband quasi-phase matching (QPM) process in a uniaxial ferroelectric crystal Ca0.28Ba0.72 Nb2O6 (CBN-28) was demonstrated with the second-harmonic wavelength range from 450 nm to 650 nm, and the relationship between the symmetries of CBN-28 and the second-harmonic patterns was experimentally and theoretically investigated based on the random anti-parallel domains in the crystal and QPM conditions. The dependences of frequency-doubled patterns on the wavelength and anisotropy of the nonlinear crystal were also studied, and the frequency-doubled photons were found to be trapped on circles. By analyzing the light-matter interacting Hamiltonians, the trapping force for second-harmonic photons was found to be centripetal and tunable by the fundamental lasers, and the variation tendencies of the rotational velocity of second-harmonic generation photons could also be predicated. The results indicate that the CBN-28 ferroelectric crystal is a promising nonlinear optical material for the generation of broadband frequency-doubled waves, and the analysis on centripetal force based on the interaction Hamiltonians may provide a novel recognition for the investigation of QPM process to be further studied. [ABSTRACT FROM AUTHOR]

In a comprehensive general introduction to the composition of physical systems in quantum mechanics, Gudder describes the quantum measurement process with the use of three types of mathematical entities: quantum observables, quantum instruments and quantum measurement models [[31]]. The unitarity of quantum evolution leads to the conservation of quantum probabilities and constitutes an essential ingredient in the proofs of many of the quantum information-theoretic no-go theorems, including the celebrated quantum no-cloning theorem. Quantum information contained in the quantum state HT ht of a qubit has some truly remarkable properties. The rapid progress achieved by quantum information science in recent decades was made possible by the realization that genuine quantum phenomena, for which their occurrences are forbidden by classical physics, are not a defect of quantum theory but are useful physical resources [[1], [3]]. [Extracted from the article]

The new paradigm of parity-time symmetry in quantum mechanics has readily been applied in the field of optics with numerous demonstrations of exotic properties in photonic systems. In this work, we report on the implementation of single frequency electrically injected distributed feedback (DFB) laser diodes based on parity-time symmetric dual gratings in a standard ridge waveguide configuration. We demonstrate enhanced modal discrimination for these devices as compared with index or gain coupled ones, fabricated in the same technology run. Optical transmission probing experiments further show asymmetric amplification in the light propagation confirming the parity-time symmetry signature of unidirectional light behavior. Another asset of these complex coupled devices is further highlighted in terms of robustness to optical feedback. [ABSTRACT FROM AUTHOR]

Excursion theory is revisited on the ground of Itô--McKean diffusions. There are raised questions about symmetries, knock-in processes, excursion local time and the non-linear version of the master formula of excursions. The questions are answered due to introducing the counting excursion technique. The technique is a synthesis of straddling at time approach, the classical, potential in spirit approach, and the theory of convolution algebra of locally integrable functions, generalized later in this work for the convolutions of σ-finite measures. Some examples are presented, including the famous problem of expressing the density of first hitting time of Ornstein-Uhlenbeck process in terms of elementary functions. [ABSTRACT FROM AUTHOR]

The article reports that workshop, supported by the EPSRC Programme Grant Symmetries and Correspondences, involved leading researchers working in adelic, affine, algebraic, anabelian, arithmetic, birational, complex, derived, enumerative, local, non-commutative, motivic, model theoretical, padic, real, symplectic, and tropical geometries.

The present article investigates the Lorentz-Poincaré covariance properties of the generalized Dirac equation for quarks endowed, besides the half-integer spin, with "color", a Z3-graded discrete variable. Thus to the the Z2 X-Z2 symmetry of the Dirac equation, corresponding to the double-valued spin variable and the charge conjugation imposing the particle-antiparticle duality, we shall add an extra Z3 symmetry describing the color variable. The difference with currently accepted QCD is that instead of three Dirac spinors carrying different colors, the generalized equation introduced in ([14], [6], [7], [9]) attributes color variables to double-valued Pauli spinors first, and the charge conjugation next, creating 12-component wave functions. The 3 X 3 generators of the SU(3) color Lie algebra appear spontaneously. The invariance under Z3-graded spinorial representation of the Lorentz-Poincaré algebra is investigated. It leads to the enlargement of symmetry by introduction of new degrees of freedom, corresponding to extra Z2-Z3 symmetry, which we attribute to the existence of three families with two avors in each ([12], [13]). The orbital representation of Z3-graded Lorentz-Poincaré algebra is constructed using the enlarged Z3-graded Minkowskian space-time M4 X Z3. Matrix and differential operator representations are presented in extenso, along with the generalized Casimir operators. [ABSTRACT FROM AUTHOR]

We have obtained the approximate analytical solutions of the nonrelativistic Hydrogen-like atoms such as ( He + , Li 2 + and Be +) and neutral atoms such as ( 2 2 Na , 12 C and 158 Au) atoms with a newly proposed generalized perturbed Yukawa potential with centrifugal barrier (GPYPCB) model using the generalized Bopp's shift method and standard perturbation theory in the symmetries of noncommutative three-dimensional real space phase (NC: 3D-RSP). By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and generalized Hamiltonian operator for all orbital quantum numbers ℓ in the symmetries of NC: 3D-RSP. The potential is a superposition of the perturbed Yukawa potential and new terms proportional with (exp (− 2 a r) r 4 , exp (− 2 a r) r 3 , exp (− a r) r 3  and  exp (− a r) r 2 ) appear as a result of the effects of noncommutativity properties of space and phase on the perturbed Yukawa potential model. The obtained energy eigenvalues appear as functions of the generalized Gamma function, the discreet atomic quantum numbers (j , n , l , s  and  m) , two infinitesimal parameters (Θ , 𝜃 ¯) , which are induced by (position–position and phase–phase). In addition, the dimensional parameters (a , V 0 , V 1 , α) of perturbed Yukawa potential with centrifugal barrier model in NC: 3D-RSP. Furthermore, we have shown that the corresponding Hamiltonian operator in (NC: 3D-RSP) symmetries is the sum of the Hamiltonian operator of perturbed Yukawa potential model and the two operators are modified spin–orbit interaction and the modified Zeeman operator for the previous Hydrogenic and neutral atoms. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the learning of generalised policies for probabilistic and classical planning problems using Action Schema Networks (ASNets). The ASNet is a neural network architecture that exploits the relational structure of (P)PDDL planning problems to learn a common set of weights that can be applied to any problem in a domain. By mimicking the actions chosen by a traditional, non-learning planner on a handful of small problems in a domain, ASNets are able to learn a generalised reactive policy that can quickly solve much larger instances from the domain. This work extends the ASNet architecture to make it more expressive, while still remaining invariant to a range of symmetries that exist in PPDDL problems. We also present a thorough experimental evaluation of ASNets, including a comparison with heuristic search planners on seven probabilistic and deterministic domains, an extended evaluation on over 18,000 Blocksworld instances, and an ablation study. Finally, we show that sparsity-inducing regularisation can produce ASNets that are compact enough for humans to understand, yielding insights into how the structure of ASNets allows them to generalise across a domain. [ABSTRACT FROM AUTHOR]

In this paper the q-deformed Schrödinger equation is derived from the q-translation symmetry in space. The correct unitary q-translation operator is constructed for q-deformed quantum mechanics with q-translation symmetry. The supersymmetric q-deformed quantum mechanics with q-translation symmetry is also discussed. [ABSTRACT FROM AUTHOR]

The Klein–Gordon equation with equal scalar and vector potentials s (r ̂) = v (r ̂) = V (r ̂) / 2 describing the dynamics of a three-dimensional under the modified Coulomb plus inverse-square potential is considered, in the symmetries of noncommutative quantum mechanics (NCQM), using Bopp's shift method. The new energy of n th excited state E n c − n (a , b , n , j , l , m) is obtained as a function of the shift energy Δ E i s (n , j , l , s , m) and E n is obtained via first-order perturbation theory in the three-dimensional noncommutative real space (NC: 3D-RS) symmetries instead of solving modified Klein–Gordon equation (MKGE) with the Weyl–Moyal star product. It is found that the perturbative solutions of discrete spectrum depended by the Gamma function, the discreet atomic quantum numbers (j , l , s , m) and the potential parameters (A and B), in addition to noncommutativity parameters (𝜃 and σ), which are induced with the effect of (space–space) noncommutativity properties. [ABSTRACT FROM AUTHOR]

Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can stabilize fragile Bloch bands that challenge our very notion of topology: Although answering to the most basic definition of topology, one can trivialize these bands through the addition of trivial Bloch bands. Here, we fully characterize the symmetry properties of the response of an acoustic metamaterial to establish the fragile nature of the low-lying Bloch bands. Additionally, we present a spectral signature in the form of spectral flow under twisted boundary conditions. [ABSTRACT FROM AUTHOR]

We present six significant open problems in Pure Inductive Logic, together with their background and current status, with the intention of raising awareness and leading ultimately to their resolution. [ABSTRACT FROM AUTHOR]

Highlights from the article: 121st Statistical Mechanics Conference Rutgers University, Busch Campus, Hill Center Room 114, Sunday, May 12, 2019-Tuesday May 14, 2019 Guests of Honor: Curtis Callan, Nigel Goldenfeld, and Horng-Tzer Yau Abstracts and slides of the presentations of some of the invited talks as well as information about past meetings, positions wanted and available, can be obtained at: The current algebra representations of quantum many-particle Schrödinger type Hamiltonian models, their factorized structure and integrability Application of solution of the quantum kinetic equations for information technology.

The search for solutions of Schrödinger equation (SE) with physically motivated potential models has led to the discovery of new physical and chemical phenomena. For example, the pseudoharmonic oscillator potential (PHOP) has a very interesting history: it is often used to compute bound-state normalizations and energy levels of some diatomic molecules. This research has been divided into two parts. Firstly, we have converted the mechanical properties related to the force constant, the equilibrium bond length, the orthonormalized wave function and the energy eigenvalues to the corresponding atomic properties, which include the dissociation energy and equilibrium intermolecular separation for the purpose of applying to the homonuclear diatomic molecules, such as O2, N2 and H2, and heteronuclear diatomic molecules, such as CH and ScH, under 2D-PHOP. Secondly, we have investigated some aspects of the modified 2D-PHOP (2DMPHOP) in noncommutative 2D real space-phase (NC: 2D-RSP) through the generalized Bopp’s shift method in the framework of parameters due to (space-phase) noncommutativity (θ,θ ) by means of the solution of the 2D-deformed SE (2D-DSE). We have reconstructed the global Hamiltonian operator for 2DMPHOP, involving three fundamental parts: the first one is the ordinary Hamiltonian operator, in commutative quantum mechanics (CQM); the second part is the spin-orbit operator нso-ph H r(θ,θ) , while the third one is the modified Zeeman operator нz-ph H (r,ϰ,σ) and corresponding energy eigenvalues by applying the perturbation method. Furthermore, we have shown that the global quantum group (GQG) of (NC: 2D-RSP) symmetries has been broken automatically and replaced by subgroup (NC: 2D-RS) under 2D-MPHOP molecules interactions. We find the energy levels of the studied homonuclear and heteronuclear diatomic molecules in CQM as special case, when we use the simultaneously two limits (θ,θ)→(0,0) [ABSTRACT FROM AUTHOR]

This paper tackles the challenging problem of constrained hexahedral meshing. An algorithm is introduced to build combinatorial hexahedral meshes whose boundary facets exactly match a given quadrangulation of the topological sphere. This algorithm is the first practical solution to the problem. It is able to compute small hexahedral meshes of quadrangulations for which the previously known best solutions could only be built by hand or contained thousands of hexahedra. These challenging quadrangulations include the boundaries of transition templates that are critical for the success of general hexahedral meshing algorithms. The algorithm proposed in this paper is dedicated to building combinatorial hexahedral meshes of small quadrangulations and ignores the geometrical problem. The key idea of the method is to exploit the equivalence between quad flips in the boundary and the insertion of hexahedra glued to this boundary. The tree of all sequences of flipping operations is explored, searching for a path that transforms the input quadrangulation Q into a new quadrangulation for which a hexahedral mesh is known. When a small hexahedral mesh exists, a sequence transforming Q into the boundary of a cube is found; otherwise, a set of pre-computed hexahedral meshes is used. A novel approach to deal with the large number of problem symmetries is proposed. Combined with an efficient backtracking search, it allows small shellable hexahedral meshes to be found for all even quadrangulations with up to 20 quadrangles. All 54, 943 such quadrangulations were meshed using no more than 72 hexahedra. This algorithm is also used to find a construction to fill arbitrary domains, thereby proving that any ball-shaped domain bounded by n quadrangles can be meshed with no more than 78 n hexahedra. This very significantly lowers the previous upper bound of 5396 n. [ABSTRACT FROM AUTHOR]

Abstract We suggest graphene and a two-dimensional (2D) Weyl semimetal (WSM) as 2D materials for the realization of a broadband coherent perfect absorber (CPA) respecting overall PT -symmetry. We also demonstrate the conditions for mutually equal amplitudes and phases of the left and right incoming waves to realize a CPA. 2D materials in our system play the role to enhance the absorption rate of a CPA once the appropriate parameters are inserted in the system. We show that a 2D WSM is more effective than graphene in obtaining the optimal conditions. We display the behavior of each parameter governing the optical system and show that optimal conditions of these parameters give rise to enhancement and possible experimental realization of a broadband CPA-laser. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the nonlocal symmetries and exact interaction solutions of the variable coefficient Korteweg–de Vries (KdV) equation are studied. With the help of pseudo-potential, we construct the high order nonlocal symmetries of the time-dependent coefficient KdV equation for the first time. In order to construct the new exact interaction solutions, two auxiliary variables are introduced, which can transform nonlocal symmetries into Lie point symmetries. Furthermore, using the Lie point symmetries of the closed system, some exact interaction solutions are obtained. For some interesting solutions, such as the soliton–cnoidal wave solutions are discussed in detail, and the corresponding 2D and 3D figures are given to illustrate their dynamic behavior. [ABSTRACT FROM AUTHOR]

In this paper, Zakharov–Kuznetsov equation is investigated for exact solutions and conservation laws. The well-known Zakharov–Kuznetsov equation contains third-order dispersion, so its validity is restricted to the waves of small amplitudes only. When the amplitude of the wave increases, the velocity and the width of the soliton deviate from the prediction of this equation. To overcome this deficiency, higher-order dispersion term is added to the Zakharov–Kuznetsov equation. We obtain Lie point symmetries and conservation laws for this new model. Wave transformation is applied to convert the nonlinear partial differential equation into another nonlinear ordinary differential equation. Then exact solutions are computed for this with sine–cosine method and modified Kudryashov methods. Obtained solutions are new and are of significant importance in the field of plasma physics. [ABSTRACT FROM AUTHOR]

We have treated the Euclidean three-dimensional O(1) ghost model with a modified version of the effective average action (EAA) renormalization group (RG) method, developed by us. We call it Fourier–Wetterich RG approach and it is used to investigate the occurrence of a periodic condensate in terms of the functional RG. The modification involves additional terms in the ansatz of the EAA, corresponding to the Fourier-modes of the periodic condensate. The RG flow equations are derived keeping the terms up to the fourth order of the gradient expansion (GE), however the numerical calculations are conducted in the second order (or next-to-leading order, NLO) of the GE. The expansion of the flow equations around the nontrivial minimum of the local potential takes into account properly the vertices induced by the periodic condensate even if the wave function renormalization is set to be field-independent. The numerical analysis reveals several different phases with three multicritical points. [ABSTRACT FROM AUTHOR]

We propose a renormalizable T′ flavor model based on the SU (3) C × SU (3) L × U (1) X × U (1) ℒ gauge symmetry, consistent with the observed pattern of lepton masses and mixings. The small masses of the light active neutrinos are produced from an interplay of type I and type II seesaw mechanisms, which are induced by three heavy right-handed Majorana neutrinos and three SU (3) L scalar antisextets, respectively. Our model is only viable for the scenario of normal neutrino mass hierarchy, where the obtained physical observables of the lepton sector are highly consistent with the current neutrino oscillation experimental data. In addition, our model also predicts an effective Majorana neutrino mass parameter of m β ∼ 1. 4 1 5 4 1 × 1 0 − 2  eV, a Jarlskog invariant of the order of J CP ∼ − 0. 0 3 2 and a leptonic Dirac CP violating phase of δ = 2 3 8 ∘ , which is inside the 1 σ experimentally allowed range. [ABSTRACT FROM AUTHOR]

Symmetrically coupled identical oscillators were once believed to support only totally synchronous or totally asynchronous states. More recently, chimera states, in which a subset of oscillators behaves coherently while the other subset exhibits disorder, have been found in large arrays of oscillators, coupled either locally or globally. We demonstrate for the first time the existence of a chimera state with only two diffusively coupled identical oscillators, one behaving nearly periodically (coherently) and the other chaotically (incoherently). We attribute this behavior to a "master-slave" interaction, which arises via a symmetry-breaking canard explosion. [ABSTRACT FROM AUTHOR]

The article presents the chapter four of the book "The Plaid Model," by Richard Evan Schwartz. Topics include the process of creating a three-dimensional (3D) interpretation of the plaid model to group certain light points, an unlike notion of adjacency for w x w blocks that divides the plaid model, and the symmetries of spacetime diagrams.

The large 𝒩 = 4 nonlinear superconformal algebra is generated by six spin- 1 currents, four spin- 3 2 currents and one spin- 2 current. The simplest extension of these 1 1 currents is described by the 1 6 higher spin currents of spins (1 , 3 2 , 3 2 , 3 2 , 3 2 , 2 , 2 , 2 , 2 , 2 , 2 , 5 2 , 5 2 , 5 2 , 5 2 , 3). In this paper, by using the defining operator product expansions (OPEs) between the 1 1 currents and 1 6 higher spin currents, we determine the 1 6 higher spin currents (the higher spin- 1 , 3 2 currents were found previously) in terms of affine Kac–Moody spin- 1 2 , one currents in the Wolf space coset model completely. An antisymmetric second rank tensor, three antisymmetric almost complex structures or the structure constant are contracted with the multiple product of spin- 1 2 , 1 currents. The eigenvalues are computed for coset representations containing at most four boxes, at finite N and k. After calculating the eigenvalues of the zeromode of the higher spin- 3 current acting on the higher representations up to three (or four) boxes of Young tableaux in S U (N + 2) in the Wolf space coset, we obtain the corresponding three-point functions with two scalar operators at finite (N , k). Furthermore, under the large (N , k) 't Hooft-like limit, the eigenvalues associated with any boxes of Young tableaux are obtained and the corresponding three-point functions are written in terms of the 't Hooft coupling constant in simple form in addition to the two-point functions of scalars and the number of boxes. [ABSTRACT FROM AUTHOR]