The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Effective Hamiltonians and Quantum States”

Exponentiations over the quantum algebra U q ( s l 2 ( ) )

Sonia L’Innocente, Françoise Point, Carlo Toffalori (2013)

Confluentes Mathematici

Similarity:

We define and compare, by model-theoretical methods, some exponentiations over the quantum algebra U q ( s l 2 ( ) ) . We discuss two cases, according to whether the parameter q is a root of unity. We show that the universal enveloping algebra of s l 2 ( ) embeds in a non-principal ultraproduct of U q ( s l 2 ( ) ) , where q varies over the primitive roots of unity.

On the Klainerman–Machedon conjecture for the quantum BBGKY hierarchy with self-interaction

Xuwen Chen, Justin Holmer (2016)

Journal of the European Mathematical Society

Similarity:

We consider the 3D quantum BBGKY hierarchy which corresponds to the N -particle Schrödinger equation. We assume the pair interaction is N 3 β 1 V ( B β ) . For the interaction parameter β ( 0 , 2 / 3 ) , we prove that, provided an energy bound holds for solutions to the BBKGY hierarchy, the N limit points satisfy the space-time bound conjectured by S. Klainerman and M. Machedon [45] in 2008. The energy bound was proven to hold for β ( 0 , 3 / 5 ) in [28]. This allows, in the case β ( 0 , 3 / 5 ) , for the application of the Klainerman–Machedon...

Quantum expanders and geometry of operator spaces

Gilles Pisier (2014)

Journal of the European Mathematical Society

Similarity:

We show that there are well separated families of quantum expanders with asymptotically the maximal cardinality allowed by a known upper bound. This has applications to the “growth" of certain operator spaces: It implies asymptotically sharp estimates for the growth of the multiplicity of M N -spaces needed to represent (up to a constant C > 1 ) the M N -version of the n -dimensional operator Hilbert space O H n as a direct sum of copies of M N . We show that, when C is close to 1, this multiplicity grows...

C * -basic construction between non-balanced quantum doubles

Qiaoling Xin, Tianqing Cao (2024)

Czechoslovak Mathematical Journal

Similarity:

For finite groups X , G and the right G -action on X by group automorphisms, the non-balanced quantum double D ( X ; G ) is defined as the crossed product ( X op ) * G . We firstly prove that D ( X ; G ) is a finite-dimensional Hopf C * -algebra. For any subgroup H of G , D ( X ; H ) can be defined as a Hopf C * -subalgebra of D ( X ; G ) in the natural way. Then there is a conditonal expectation from D ( X ; G ) onto D ( X ; H ) and the index is [ G ; H ] . Moreover, we prove that an associated natural inclusion of non-balanced quantum doubles is the crossed product by the...

Covariantization of quantized calculi over quantum groups

Seyed Ebrahim Akrami, Shervin Farzi (2020)

Mathematica Bohemica

Similarity:

We introduce a method for construction of a covariant differential calculus over a Hopf algebra A from a quantized calculus d a = [ D , a ] , a A , where D is a candidate for a Dirac operator for A . We recover the method of construction of a bicovariant differential calculus given by T. Brzeziński and S. Majid created from a central element of the dual Hopf algebra A . We apply this method to the Dirac operator for the quantum SL ( 2 ) given by S. Majid. We find that the differential calculus obtained by our...

Right coideal subalgebras of U q + ( 𝔰𝔬 2 n + 1 )

V. K. Kharchenko (2011)

Journal of the European Mathematical Society

Similarity:

We give a complete classification of right coideal subalgebras that contain all grouplike elements for the quantum group U q + ( 𝔰𝔬 2 n + 1 ) provided that q is not a root of 1. If q has a finite multiplicative order t > 4 ; this classification remains valid for homogeneous right coideal subalgebras of the Frobenius–Lusztig kernel u q + ( 𝔰𝔬 2 n + 1 ) . In particular, the total number of right coideal subalgebras that contain the coradical equals ( 2 n ) ! ! ; the order of the Weyl group defined by the root system of type B n .

The basic construction from the conditional expectation on the quantum double of a finite group

Qiaoling Xin, Lining Jiang, Zhenhua Ma (2015)

Czechoslovak Mathematical Journal

Similarity:

Let G be a finite group and H a subgroup. Denote by D ( G ; H ) (or D ( G ) ) the crossed product of C ( G ) and H (or G ) with respect to the adjoint action of the latter on the former. Consider the algebra D ( G ) , e generated by D ( G ) and e , where we regard E as an idempotent operator e on D ( G ) for a certain conditional expectation E of D ( G ) onto D ( G ; H ) . Let us call D ( G ) , e the basic construction from the conditional expectation E : D ( G ) D ( G ; H ) . The paper constructs a crossed product algebra C ( G / H × G ) G , and proves that there is an algebra isomorphism between...

The Grothendieck ring of quantum double of quaternion group

Hua Sun, Jia Pang, Yanxi Shen (2024)

Czechoslovak Mathematical Journal

Similarity:

Let 𝕜 be an algebraically closed field of characteristic p 2 , and let Q 8 be the quaternion group. We describe the structures of all simple modules over the quantum double D ( 𝕜 Q 8 ) of group algebra 𝕜 Q 8 . Moreover, we investigate the tensor product decomposition rules of all simple D ( 𝕜 Q 8 ) -modules. Finally, we describe the Grothendieck ring G 0 ( D ( 𝕜 Q 8 ) ) by generators with relations.

Truncation and Duality Results for Hopf Image Algebras

Teodor Banica (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

Associated to an Hadamard matrix H M N ( ) is the spectral measure μ ∈ [0,N] of the corresponding Hopf image algebra, A = C(G) with G S N . We study a certain family of discrete measures μ r [ 0 , N ] , coming from the idempotent state theory of G, which converge in Cesàro limit to μ. Our main result is a duality formula of type 0 N ( x / N ) p d μ r ( x ) = 0 N ( x / N ) r d ν p ( x ) , where μ r , ν r are the truncations of the spectral measures μ,ν associated to H , H t . We also prove, using these truncations μ r , ν r , that for any deformed Fourier matrix H = F M Q F N we have μ = ν.

A class of quantum doubles of pointed Hopf algebras of rank one

Hua Sun, Yueming Li (2023)

Czechoslovak Mathematical Journal

Similarity:

We construct a class of quantum doubles D ( H D n ) of pointed Hopf algebras of rank one H 𝒟 . We describe the algebra structures of D ( H D n ) by generators with relations. Moreover, we give the comultiplication Δ D , counit ε D and the antipode S D , respectively.

Measure-geometric Laplacians for partially atomic measures

Marc Kesseböhmer, Tony Samuel, Hendrik Weyer (2020)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Motivated by the fundamental theorem of calculus, and based on the works of W. Feller as well as M. Kac and M. G. Kreĭn, given an atomless Borel probability measure η supported on a compact subset of U. Freiberg and M. Zähle introduced a measure-geometric approach to define a first order differential operator η and a second order differential operator Δ η , with respect to η . We generalize this approach to measures of the form η : = ν + δ , where ν is non-atomic and δ is finitely supported. We determine...

Cluster ensembles, quantization and the dilogarithm

Vladimir V. Fock, Alexander B. Goncharov (2009)

Annales scientifiques de l'École Normale Supérieure

Similarity:

A cluster ensemble is a pair ( 𝒳 , 𝒜 ) of positive spaces (i.e. varieties equipped with positive atlases), coming with an action of a symmetry group Γ . The space 𝒜 is closely related to the spectrum of a cluster algebra [12]. The two spaces are related by a morphism p : 𝒜 𝒳 . The space 𝒜 is equipped with a closed 2 -form, possibly degenerate, and the space 𝒳 has a Poisson structure. The map p is compatible with these structures. The dilogarithm together with its motivic and quantum avatars plays a central...