New Type Of Symmetry Research Articles

Anomaly inflow for dipole symmetry and higher form foliated field theories

In accordance with recent progress of fracton topological phases, unusual topological phases of matter hosting fractionalized quasiparticle excitations with mobility constraints, new type of symmetry is studied — multipole symmetry, associated with conservation of multipoles. Based on algebraic relation between dipole and global charges, we introduce a series of (d + 1)-dimensional BF theories with p-form gauge fields, which admit dipole of spatially extended excitations, and study their physical properties. We elucidate that gauge invariant loops have unusual form, containing linear function of the spatial coordinate, which leads to the position dependent braiding statistics and unusual ground state degeneracy dependence on the system size. We also show that the theories exhibit a mixed ’t Hooft anomaly between p-form and (d − p)-form dipole symmetries, which is canceled by an invertible theory defined in one dimensional higher via anomaly inflow mechanism.

Ren-integrable and ren-symmetric integrable systems

A new type of symmetry, ren-symmetry, describing anyon physics and corresponding topological physics, is proposed. Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such as super-symmetric quantum mechanics, super-symmetric gravity, super-symmetric string theory, super-symmetric integrable systems and so on. Super-symmetry and Grassmann numbers are, in some sense, dual conceptions, and it turns out that these conceptions coincide for the ren situation, that is, a similar conception of ren-number (R-number) is devised for ren-symmetry. In particular, some basic results of the R-number and ren-symmetry are exposed which allow one to derive, in principle, some new types of integrable systems including ren-integrable models and ren-symmetric integrable systems. Training examples of ren-integrable KdV-type systems and ren-symmetric KdV equations are explicitly given.

Noninvertible Symmetries from Holography and Branes.

We propose a systematic approach to deriving symmetry generators of quantum field theories in holography. Central to this analysis are the Gauss law constraints in the Hamiltonian quantization of symmetry topological field theories (SymTFTs), which are obtained from supergravity. In turn, we realize the symmetry generators from world-volume theories of D-branes in holography. Our main focus is on noninvertible symmetries, which have emerged in the past year as a new type of symmetry in d≥4 QFTs. We exemplify our proposal in the holographic confinement setup, dual to 4D N=1 Super-Yang Mills. In the brane picture, the fusion of noninvertible symmetries naturally arises from the Myers effect on D-branes. In turn, their action on line defects is modeled by the Hanany-Witten effect.

A new symmetry for large deviation functions of time-integrated dynamical variables

A new type of symmetry in the large deviation function of a time-integrated current is introduced. This current is different from the fluctuating entropy production for which the large deviation function is symmetric in the content of the fluctuation theorem. The origin of this symmetry, similar to that of the Gallavotti-Cohen-Evans-Morriss symmetry, is related to time-reversal. The symmetry is more unveiled when one performs an appropriate grouping of stochastic trajectories in the space of microscopic configurations. It turns out that the characteristic polynomial of the modified generator of this current is not symmetric; however, its minimum eigenvalue is symmetric.

Families of symmetries and the hydrogen atom

We study a new type of symmetry for the hydrogen atom involving algebraic families of groups parametrized by the energy value in the time-independent Schrödinger equation. We construct an algebraic family of Harish-Chandra modules from the solutions of the Schrödinger equation, and we characterize this family. We show that the subspaces of physical states may be obtained from our algebraic family using a Jantzen filtration, and we relate our algebraic methods with spectral theory and scattering theory using the limiting absorption principle.

Qualitative Theory of Two-Dimensional Polynomial Dynamical Systems

A qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis of a discriminant criterion elaborated in the paper. This criterion enables one to pick up a single parameter that makes it possible to identify all feasible solution classes as well as the DS critical and singular points and solutions. The integrability of the considered DS family is established. Nine specific solution classes are identified. In each class, clear types of symmetry are determined and visualized and it is discussed how transformations between the solution classes create new types of symmetries. Visualization is performed as series of phase portraits revealing all possible catastrophic scenarios that result from the transition between the solution classes.

On certifying the UNSAT result of dynamic symmetry-handling-based SAT solvers

SAT solvers are nowadays used in many applications where the UNSAT result has a special meaning that is at time critical. SAT instances sometimes exhibit symmetries which can be exploited to produce short proofs that would have been exponential for resolution alone. However, current unsatisfiability proof formats do not support symmetrical learning on which dynamic symmetry handling is based. We present in this paper a new proof format called DSRUP (Delete Symmetry Reverse Unit Propagation) which is an extension of DRUP (Delete Reverse Unit Propagation) and that is devised to certify UNSAT claims of SAT solvers implementing symmetrical learning. We first show that the problem of verifying symmetries of a CNF formula is Turing NP-hard. This led us to the definition of a new type of symmetry called RUP-symmetry, a class of symmetries more general than syntactic symmetries that can be efficiently checked. The DSRUP proof format is formally described and a verification algorithm is provided to validate DSRUP certificates. Finally, we provide experimental results obtained with the state-of-the-art dynamic symmetry-handling-based SAT solvers on unsatisfiable symmetric benchmarks drawn from SAT competitions, using an implementation of the DSRUP checking algorithm.

Loss compensation symmetry in dimers made of gain and lossy nanoparticles

The eigenmodes in a two-dimensional dimer made of gain and lossy nanoparticles have been investigated within an exact analytical approach. It has been shown that there are eigenmodes for which all Joule losses are exactly compensated by the gain. Among such solutions there are solutions with a new type of symmetry, which we refer to as loss compensation symmetry, as well as well-known parity–time (PT) symmetric solutions. Unlike PT symmetric ones, the modes with loss compensation symmetry allow one to achieve full loss compensation with significantly less gain that in the case of PT symmetry. This effect paves the way to new loss compensation methods in optics.

Universality of modular symmetries in two-dimensional magnetotransport

The quantum Hall effect has bagged several Nobel prizes and is a cornerstone of modern metrology, but after four decades it continues to strain our understanding of quantum physics. This comprehensive review of scaling experiments provides substantial support for the conjecture that the morass of Hall data conceals a new type of symmetry, known as modular symmetry [C. A. L\utken and G. G. Ross, Phys. Rev. B 45, 11837 (1992)]. These infinite discrete symmetries are central to many recent developments in mathematics and string theory, but have not previously been seen in nature.

Nonradial sign changing solutions to Lane–Emden problem in an annulus

In this paper we prove the existence of continua of nonradial solutions for the Lane–Emden equation in the annulus. In a first result we show that there are infinitely many global continua detaching from the curve of radial solutions with any prescribed number of nodal zones. Next, using the fixed point index in cone, we produce nonradial solutions with a new type of symmetry. This result also applies to solutions with fixed signed, showing that the set of solutions to the Lane–Emden problem has a very rich and complex structure.

Kolmogorov goodness-of-fit test for S-symmetric distributions in climate and weather modeling

Statistical data treatment is an essential part of climate and weather modeling. The Kolmogorov goodness-of-fit test is a widely applicable statistical method to determine the cumulative distribution function of a continuous random variable, e.g., a precipitation level, wind force, etc. In this paper, the authors consider a problem of goodness-of-fit testing involving additional information about S-symmetry of the cumulative distribution function and its influence on the Kolmogorov statistic distributions. A definition of S-symmetry is given; it is a generalized classical definition of distribution symmetry. It is proved that any continuous increasing cumulative distribution function is S-symmetric. A uniform distribution is considered as an example of an S-symmetric distribution. A modification of the Kolmogorov statistic using additional information about the new type of symmetry is proposed. The exact and asymptotic distributions under the null and the alternative hypothesis of the modified statistics are described. The authors also provide an example which proves that the modified test is more powerful than the non-modified one. The new test is used to check the hypothesis of a uniform distribution of the average sum of precipitation.

Critical Casimir effect in the Ising strips with standard normal and ordinary boundary conditions and the grain boundary

We consider critical Casimir force in the Ising strips with boundary conditions defined by standard normal and ordinary surface universality classes containing also the internal grain boundary. Using exact variational approach of Mikheev and Fisher we have elaborated on behaviors of Casimir amplitudes Δ++(g), ΔOO(g) and Δ+O(g), corresponding to normal–normal, ordinary–ordinary and mixed normal–ordinary boundary conditions, respectively, with g as a strength of the grain boundary. Closed analytic results describe Casimir amplitudes Δ++(g) and ΔOO(g) as continuous functions of the grain boundary’s strength g, changing the character of the Casimir force from repulsive to attractive and vice versa for certain domains of g. Present results reveal a new type of symmetry between Casimir amplitudes Δ++(g) and ΔOO(g). Unexpectedly simple constant result for the Casimir amplitude Δ+O(g)=π12 we have comprehensively interpreted in terms of equilibrium states of the present Ising strip as a complex interacting system comprising two sub-systems. Short-distance expansions of energy density profiles in the vicinity of the grain boundary reveal new distant-wall correction amplitudes that we examined in detail. Analogy of present considerations with earlier more usual short-distance expansions near one of the (N), (O) and (SB) boundaries, as well as close to surfaces with variable boundary conditions refers to the set of scaling dimensions appearing in the present calculations but also to the discovery of the de Gennes–Fisher distant wall correction amplitudes.

Bicomplex hamiltonian systems in quantum mechanics

We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrödinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define, in a natural way, a separate class of time reversal operator. However, the induced parity ()-time ()-symmetric models turn out to be mutually incompatible, except for two of them which could be chosen uniquely. The latter models are then explored by working within an extended phase space. Applications to the problems of harmonic oscillator, inverted oscillator and isotonic oscillator are considered and many new interesting properties are uncovered for the new types of symmetries.

Compass models: Theory and physical motivations

Compass models are theories of matter in which the couplings between the internal spin (or other relevant field) components are inherently spatially (typically, direction) dependent. A simple illustrative example is furnished by the 90\ifmmode^\circ\else\textdegree\fi{} compass model on a square lattice in which only couplings of the form ${\ensuremath{\tau}}_{i}^{x}{\ensuremath{\tau}}_{j}^{x}$ (where ${{\ensuremath{\tau}}_{i}^{a}{}}_{a}$ denote Pauli operators at site $i$) are associated with nearest-neighbor sites $i$ and $j$ separated along the $x$ axis of the lattice while ${\ensuremath{\tau}}_{i}^{y}{\ensuremath{\tau}}_{j}^{y}$ couplings appear for sites separated by a lattice constant along the $y$ axis. Similar compass-type interactions can appear in diverse physical systems. For instance, compass models describe Mott insulators with orbital degrees of freedom where interactions sensitively depend on the spatial orientation of the orbitals involved as well as the low-energy effective theories of frustrated quantum magnets, and a host of other systems such as vacancy centers, and cold atomic gases. The fundamental interdependence between internal (spin, orbital, or other) and external (i.e., spatial) degrees of freedom which underlies compass models generally leads to very rich behaviors, including the frustration of (semi-)classical ordered states on nonfrustrated lattices, and to enhanced quantum effects, prompting, in certain cases, the appearance of zero-temperature quantum spin liquids. As a consequence of these frustrations, new types of symmetries and their associated degeneracies may appear. These intermediate symmetries lie midway between the extremes of global symmetries and local gauge symmetries and lead to effective dimensional reductions. In this article, compass models are reviewed in a unified manner, paying close attention to exact consequences of these symmetries and to thermal and quantum fluctuations that stabilize orders via order-out-of-disorder effects. This is complemented by a survey of numerical results. In addition to reviewing past works, a number of other models are introduced and new results established. In particular, a general link between flat bands and symmetries is detailed.

Optimal class-specific witnesses for three-qubit entanglement from Greenberger-Horne-Zeilinger symmetry

Recently, a new type of symmetry for three-qubit quantum states was introduced, the so-called Greenberger-Horne-Zeilinger (GHZ) symmetry. It includes the operations which leave the three-qubit standard GHZ state unchanged. This symmetry is powerful as it yields families of mixed states that are, on the one hand, complex enough from the physics point of view and, on the other hand, simple enough mathematically so that their properties can be characterized analytically. We show that by using the properties of GHZ-symmetric states it is straightforward to derive optimal witnesses for detecting class-specific entanglement in arbitrary three-qubit states.

Graph of a Nearring with Respect to an Ideal

We introduce a concept called the graph of a nearring N with respect to an ideal I of N denoted by G I (N). Then we define a new type of symmetry called ideal symmetry of G I (N). The ideal symmetry of G I (N) implies the symmetry determined by the automorphism group of G I (N). We prove that if I is a 3-prime ideal of a zero-symmetric nearring N then G I (N) is ideal symmetric. Under certain conditions, we find that if G I (N) is ideal symmetric then I is 3-prime. Finally, we deduce that if N is an equiprime nearring then the prime graph of N is ideal symmetric.

Spin control in semiconductor quantum wires: Rashba and Dresselhaus interaction

Conselleria d’Educaci´o i Cultura, E-07004 Palma de Mallorca, Spain(Dated: November 30, 2008)We show that spin-flip rotation in a semiconductor quantum wire, caused by the Rashba andthe Dresselhaus interactions (both of arbitrary strengths), can be suppressed by dint of an in-planemagnetic field. We found a new type of symmetry, which arises at a particular set of intensity andorientation of the magnetic field and explains this suppression. Based on our findings, we proposea transport experiment to measure the strengths of the Rashba and the Dresselhaus interactions.

Julius Erich Wess

Julius Erich Wess

Duality in permutation state spaces and the dual search algorithm

Geometrical symmetries are commonly exploited to improve the efficiency of search algorithms. A new type of symmetry in permutation state spaces, duality, is introduced. Each state has a dual state. Both states share important attributes such as their distance to the goal. Given a state S, it is shown that an admissible heuristic of the dual state of S is an admissible heuristic for S. This provides opportunities for additional heuristic evaluations. An exact definition of the class of problems where duality exists is provided. A new search algorithm, dual search, is presented which switches between the original state and the dual state when it seems likely that the switch will improve the chance of reaching the goal faster. The decision of when to switch is very important and several policies for doing this are investigated. Experimental results show significant improvements for a number of applications, for using the dual state's heuristic evaluation and/or dual search.

Discontinuous maps exhibiting symmetry Lebesgue-almost everywhere

In this paper we analyse the existence of a certain type of symmetry in the context of discontinuous maps. The classical notions of symmetry cannot be applied due to the existence of discontinuities and a broader version using a measure-theory perspective is introduced. We show that a group structure is also present under the new type of symmetry and derive results which are analogous in nature to results in the theory of continuous maps. Our motivation stems from examples of symmetric patterns arising in simulations with the Goetz map.