The Experts below are selected from a list of 1134 Experts worldwide ranked by ideXlab platform
G Niccoli - One of the best experts on this subject based on the ideXlab platform.
-
non diagonal open spin 1 2 xxz quantum chains by separation of variables complete spectrum and matrix elements of some quasi local operators
Journal of Statistical Mechanics: Theory and Experiment, 2012Co-Authors: G NiccoliAbstract:The integrable quantum models, associated with the transfer matrices of the 6-vertex reflection algebra for spin-1/2 representations, are studied in this paper. In the framework of Sklyanin’s quantum separation of variables (SOV), we provide the complete characterization of the eigenvalues and eigenstates of the transfer matrix and the proof of the simplicity of the transfer matrix spectrum. Moreover, we use these integrable quantum models as further key examples for which to develop a method in the SOV framework to compute matrix elements of local operators. This method is based on the resolution of the quantum inverse problem (i.e. the reconstruction of local operators in terms of the quantum separate variables) plus the computation of the action of separate Covectors on separate vectors. In particular, for these integrable quantum models, which in the homogeneous limit reproduce the open spin-1/2 XXZ quantum chains with non-diagonal boundary conditions, we have obtained the SOV-reconstruction for a class of quasi-local operators and determinant formulae for the Covector–vector actions. As a consequence of these findings we provide one determinant formula for the matrix elements of this class of reconstructed quasi-local operator on transfer matrix eigenstates.
-
non diagonal open spin 1 2 xxz quantum chains by separation of variables complete spectrum and matrix elements of some quasi local operators
arXiv: Mathematical Physics, 2012Co-Authors: G NiccoliAbstract:The integrable quantum models, associated to the transfer matrices of the 6-vertex reflection algebra for spin 1/2 representations, are studied in this paper. In the framework of Sklyanin's quantum separation of variables (SOV), we provide the complete characterization of the eigenvalues and eigenstates of the transfer matrix and the proof of the simplicity of the transfer matrix spectrum. Moreover, we use these integrable quantum models as further key examples for which to develop a method in the SOV framework to compute matrix elements of local operators. This method has been introduced first in [1] and then used also in [2], it is based on the resolution of the quantum inverse problem (i.e. the reconstruction of all local operators in terms of the quantum separate variables) plus the computation of the action of separate Covectors on separate vectors. In particular, for these integrable quantum models, which in the homogeneous limit reproduce the open spin-1/2 XXZ quantum chains with non-diagonal boundary conditions, we have obtained the SOV-reconstructions for a class of quasi-local operators and determinant formulae for the Covector-vector actions. As consequence of these findings we provide one determinant formulae for the matrix elements of this class of reconstructed quasi-local operators on transfer matrix eigenstates.
Yin Chen - One of the best experts on this subject based on the ideXlab platform.
-
relations between modular invariants of a vector and a Covector in dimension two
Canadian Mathematical Bulletin, 2020Co-Authors: Yin ChenAbstract:We exhibit a set of generating relations for the modular invariant ring of a vector and a Covector for the two-dimensional general linear group over a finite field.
-
The second main theorem for the two-dimensional general linear group over a finite field
arXiv: Commutative Algebra, 2020Co-Authors: Yin ChenAbstract:We exhibit a set of generating relations for the modular invariant ring of a vector and a Covector for the two-dimensional general linear group over a finite field.
-
on modular invariants of a vector and a Covector
Manuscripta Mathematica, 2014Co-Authors: Yin ChenAbstract:Let GL 2(F q ) be the general linear group over a finite field F q , V be the 2-dimensional natural representation of GL 2(F q ) and V * be the dual representation. We denote by \({F_{q}[V\oplus V^{\ast}]^{GL_{2}(F_{q})}}\) the corresponding invariant ring of a vector and a Covector for GL 2(F q ). In this paper, we prove that \({F_{q}[V\oplus V^{\ast}]^{GL_{2}(F_{q})}}\) is a Gorenstein algebra. This result confirms a special case (n = 2) of the recent conjecture of Bonnafe and Kemper (J Algebra 335:96–112, 2011).
-
on modular invariants of a vector and a Covector
arXiv: Commutative Algebra, 2012Co-Authors: Yin ChenAbstract:Let $SL_{2}(F_{q})$ be the special linear group over a finite field $F_{q}$, $V$ be the 2-dimensional natural representation of $SL_{2}(F_{q})$ and $V^{\ast}$ be the dual representation. We denote by $F_{q}[V\oplus V^{\ast}]^{SL_{2}(F_{q})}$ the corresponding invariant ring of a vector and a Covector for $SL_{2}(F_{q})$. In this paper, we construct a free module basis over some homogeneous system of parameters of $F_{q}[V\oplus V^{\ast}]^{SL_{2}(F_{q})}$. We calculate the Hilbert series of $F_{q}[V\oplus V^{\ast}]^{SL_{2}(F_{q})}$, and prove that it is a Gorenstein algebra. As an application, we confirm a special case of the recent conjecture of Bonnafe and Kemper in 2011.
Ralf Lehnert - One of the best experts on this subject based on the ideXlab platform.
-
Classical-physics applications for Finsler $b$ space
Bulletin of the American Physical Society, 2015Co-Authors: Joshua Foster, Ralf LehnertAbstract:Article history: Received 26 January 2015 Received in revised form 30 March 2015 Accepted 22 April 2015 Available online 24 April 2015 Editor: A. Ringwald The classical propagation of certain Lorentz-violating fermions is known to be governed by geodesics of a four-dimensional pseudo-Finsler b space parametrized by a prescribed background Covector field. This work identifies systems in classical physics that are governed by the three-dimensional version of Finsler b space and constructs a geodesic for a sample non-constant choice for the background Covector. The existence of these classical analogues demonstrates that Finsler b spaces possess applications in conventional physics, which may yield insight into the propagation of SME fermions on curved manifolds. © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.
-
Classical-physics applications for Finsler $b$ space
Physics Letters B, 2015Co-Authors: Joshua Foster, Ralf LehnertAbstract:Abstract The classical propagation of certain Lorentz-violating fermions is known to be governed by geodesics of a four-dimensional pseudo-Finsler b space parametrized by a prescribed background Covector field. This work identifies systems in classical physics that are governed by the three-dimensional version of Finsler b space and constructs a geodesic for a sample non-constant choice for the background Covector. The existence of these classical analogues demonstrates that Finsler b spaces possess applications in conventional physics, which may yield insight into the propagation of SME fermions on curved manifolds.
Joshua Foster - One of the best experts on this subject based on the ideXlab platform.
-
Classical-physics applications for Finsler $b$ space
Bulletin of the American Physical Society, 2015Co-Authors: Joshua Foster, Ralf LehnertAbstract:Article history: Received 26 January 2015 Received in revised form 30 March 2015 Accepted 22 April 2015 Available online 24 April 2015 Editor: A. Ringwald The classical propagation of certain Lorentz-violating fermions is known to be governed by geodesics of a four-dimensional pseudo-Finsler b space parametrized by a prescribed background Covector field. This work identifies systems in classical physics that are governed by the three-dimensional version of Finsler b space and constructs a geodesic for a sample non-constant choice for the background Covector. The existence of these classical analogues demonstrates that Finsler b spaces possess applications in conventional physics, which may yield insight into the propagation of SME fermions on curved manifolds. © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.
-
Classical-physics applications for Finsler $b$ space
Physics Letters B, 2015Co-Authors: Joshua Foster, Ralf LehnertAbstract:Abstract The classical propagation of certain Lorentz-violating fermions is known to be governed by geodesics of a four-dimensional pseudo-Finsler b space parametrized by a prescribed background Covector field. This work identifies systems in classical physics that are governed by the three-dimensional version of Finsler b space and constructs a geodesic for a sample non-constant choice for the background Covector. The existence of these classical analogues demonstrates that Finsler b spaces possess applications in conventional physics, which may yield insight into the propagation of SME fermions on curved manifolds.
Stavrinos P. C. - One of the best experts on this subject based on the ideXlab platform.
-
Schwarzschild-Randers solution on a Lorentz tangent bundle
2020Co-Authors: Triantafyllopoulos A., Basilakos S., Kapsabelis E., Stavrinos P. C.Abstract:In this work, we extend for the first time the spherically symmetric Schwarzschild and Schwarzschild-De Sitter solutions with a Randers-type perturbation which is generated by a Covector $A_\gamma$. This gives a locally anisotropic character to the metric and induces a deviation from the Riemannian models of gravity. A natural framework for this study is the Lorentz tangent bundle of a spacetime manifold. We apply the generalized field equations of this framework to the perturbed metric and derive the dynamics for the Covector $A_\gamma$. Finally, we find the timelike, spacelike and null paths on the Schwarzschild-Randers spacetime and we compare them with the geodesics of general relativity. The obtained solutions are new and they enrich the corresponding literature.Comment: 15 page
-
Schwarzschild-like solutions in Finsler-Randers gravity
'Springer Science and Business Media LLC', 2020Co-Authors: Triantafyllopoulos A., Basilakos S., Kapsabelis E., Stavrinos P. C.Abstract:In this work, we extend for the first time the spherically symmetric Schwarzschild and Schwarzschild-De Sitter solutions with a Finsler-Randers-type perturbation which is generated by a Covector $A_\gamma$. This gives a locally anisotropic character to the metric and induces a deviation from the Riemannian models of gravity. A natural framework for this study is the Lorentz tangent bundle of a spacetime manifold. We apply the generalized field equations to the perturbed metric and derive the dynamics for the Covector $A_\gamma$. Finally, we find the timelike, spacelike and null paths on the Schwarzschild-Randers spacetime, we solve the timelike ones numerically and we compare them with the classic geodesics of general relativity. The obtained solutions are new and they enrich the corresponding literature.Comment: 13 pages, 2 figures, to be published in EPJ
