118656911
Fine-grained uncertainty relations under relativistic motion
Among various uncertainly relations, the profound fine-grained uncertainty relation is used to distinguish the uncertainty inherent in obtaining any combination of outcomes for different measurements. In this letter, we explore this uncertainty relation in a relativistic regime. For an observer undergoing a uniform acceleration who is immersed in an Unruh thermal bath, we show that the uncertainty bound is dependent on the acceleration parameter and the choice of Unruh modes. We find that the measurements in mutually unbiased bases, sharing the same uncertainty bound in the inertial frame, could be distinguished from each other for a noninertial observer. In an alternative scenario, for the observer restricted in a single rigid cavity, we show that the uncertainty bound exhibits a periodic evolution with respect to the duration of acceleration. With properly chosen cavity parameters, the uncertainty bounds could be protected. Moreover, we find that the uncertainty bound can be degraded for specific quantum measurements to violate the bound exhibited in the nonrelativistic limit, which can be attributed to the entanglement generation between cavity modes during a particular epoch. Several implications of our results are discussed. Copyright (c) EPLA, 2018
121731174
Some algebraic identities in anomalous gauge theories
Some useful algebraic relations between the anomaly of Dmu Jmu and anomalous commutators are derived using only the canonical commutators and the equation of motion. Their applications are discussed.
17047722
Infinite Families of Gauge-Equivalent R-Matrices and Gradations of Quantized Affine Algebras
Associated with the fundamental representation of a quantum algebra such as Uq(A1) or Uq(A2), there exist infinitely many gauge-equivalent R-matrices with different spectralparameter dependences. It is shown how these can be obtained by examining the infinitely many possible gradations of the corresponding quantum affine algebras, such as and , and explicit formulae are obtained for those two cases. Spectral-dependent similarity (gauge) transformations relate the R-matrices in different gradations, Nevertheless, the choice of gradation can be physically significant, as is illustrated in the case of quantum affine Toda field theories.
1264030
Elliptic Gaudin models and elliptic KZ equations
The Gaudin models based on the face-type elliptic quantum groups and the XYZ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik–Zamolodchikov equations and their solutions are given.
119694191
Construction of basis vectors for symmetric irreducible representations of O(5) $ \supset$ O(3)
Abstract.A recursive method for the construction of symmetric irreducible representations of $ O(2l+1)$ in the $ O(2l+1)\supset O(3)$ basis for identical boson systems is proposed. The formalism is realized based on the group chain $ U(2l+1)\supset U(2l-1)\otimes U(2)$ , of which the symmetric irreducible representations are simply reducible. The basis vectors for symmetric irreducible representations of the $ O(2l+1)\supset O(2l-1)\otimes U(1)$ can easily be constructed from those of U(2l + 1) $ \supset$U(2l - 1) ⊗ U(2) $ \supset$O(2l - 1) ⊗ U(1) with no l -boson pairs, namely with the total boson number exactly equal to the seniority number in the system, from which one can construct symmetric irreducible representations of $ O(2l+1)$ in the $ O(2l-1)\otimes U(1)$ basis when all symmetric irreducible representations of O(2l - 1) are known. As a starting point, basis vectors of symmetric irreducible representations of O(5) are constructed in the $ O_{1}(3)\otimes U(1)$ basis, where $ O_{1}(3)\equiv O(2l-1)$ , when l = 2 , which is generated not by the angular momentum operators of the d -boson system, but by the operators constructed from d -boson creation (annihilation) operators $ d^{\dagger}_{\mu}$ ( $ d_{\mu}$ with $ \mu=1$ , 0, -1 . Matrix representations of $ O(5)\supset O_{1}(3)\otimes U(1)$ , together with the elementary Wigner coefficients, are presented. After the angular momentum projection, a three-term relation in determining the expansion coefficients of the $ O(5)\supset O(3)$ basis vectors, where the O(3) group is generated by the angular momentum operators of the d -boson system, in terms of those of $ O_{1}(3)\otimes U(1)$ is derived. The eigenvectors of the projection matrix with zero eigenvalues constructed according to the three-term relation completely determine the basis vectors of $ O(5)\supset O(3)$ . Formulae for evaluating the elementary Wigner coefficients of $ O(5)\supset O(3)$ are derived explicitly. Analytical expressions of some elementary Wigner coefficients of $ O(5)\supset O(3)$ for the coupling $ (\tau 0)\otimes(1 0)$ with resultant angular momentum quantum number L = 2$ \tau$ + 2 - k for $ k=0,2,3,\ldots,6$ with a multiplicity 2 case for k = 6 are presented.
2107479
Local Quasitriangular Hopf Algebras
We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. The category of modules with finite cycles over a local quasitriangular Hopf algebra is a braided tensor category.
41782509
Direct detection of baryogenesis mechanism from squark decays at LHC
We investigate the feasibility of directly detecting a generation mechanism of the cosmic baryon asymmetry by repeating the same particle physics process inside the LHC. We propose a framework with R-parity and CP violating squark decays responsible for baryogenesis, which can be embedded in supersymmetric models and is partly motivated by naturalness. We argue that the baryon number generation here is closely related to lepton charge asymmetry on the resonance. We emphasize the importance of the single charged lepton plus multijet channel in the absence of significant missing energy in search of such a scenario.
15694234
Warm Dark Matter in Low Scale Left-Right Theory
We investigate the viability of having dark matter in the minimal left-right symmetric theory. We find the lightest right-handed neutrino with a mass around keV as the only viable candidate consistent with a TeV scale of left-right symmetry. In order to account for the correct relic density with such low scales, the thermal overproduction of the dark matter in the early universe is compensated by a sufficient late entropy production due to late decay of heavier right-handed neutrinos. We point out that the presence of the right-handed charge-current interactions, operative around the QCD phase transition, has a crucial impact on the amount of dilution, as does the nature of the phase transition itself. A careful numerical study, employing the Boltzmann equations, reveals the existence of a narrow window for the right-handed gauge boson mass, possibly within the reach of LHC (in disagreement with a previous study). We also elaborate on a variety of astrophysical, cosmological and low energy constraints on this scenario.
117856805
A cosmic ray test platform based on high time resolution MRPC technology
In order to test the performance of detector prototypes in a laboratory environment, we design and build a large area (90 cm×52 cm) test platform for cosmic rays based on a well-designed Multi-gap Resistive Plate Chamber (MRPC) with excellent time resolution and a high detection efficiency for minimum ionizing particles. The time resolution of the MRPC module used is tested to be ~80 ps, and the position resolution along the strip is ~5 mm, while the position resolution perpendicular to the strip is ~12.7 mm. The platform constructed by four MRPC modules can be used for tracking cosmic rays with a spatial resolution of ~6.3 mm, and provide a reference time ~40 ps.
30742433
Yukawa bound states of a large number of fermions
A bstractWe consider the bound state problem for a field theory that contains a Dirac fermion χ that Yukawa couples to a (light) scalar field ϕ. We are interested in bound states with a large number N of χ particles. A Fermi gas model is used to numerically determine the dependence of the radius R of these bound states on N and also the dependence of the binding energy on N. Since scalar interactions with relativistic χ’s are suppressed two regimes emerge. For modest values of N the state is composed of non-relativistic χ particles. In this regime as N increases R decreases. Eventually the core region becomes relativistic and the size of the state starts to increase as N increases. As a result, for fixed Yukawa coupling and χ mass, there is a minimum sized state that occurs roughly at the value of N where the core region first becomes relativistic. We also compute an elastic scattering form factor that can be relevant for direct detection if the dark matter is composed of such χ particles.
119108763
Magnetic field effect on the phase transition in AdS soliton spacetime
We investigate the scalar perturbations in an anti-de Sitter soliton background coupled to a Maxwell field via marginally stable modes. In the probe limit, we study the magnetic field effect on the holographic insulator/superconductor phase transition numerically and analytically. The condensate will be localized in a finite circular region for any finite constant magnetic field. Near the critical point, we find that there exists a simple relation among the critical chemical potential, magnetic field, the charge, and mass of the scalar field. This relation indicates that the presence of the magnetic field causes the transition from insulator to superconductor to be difficult.