Results 1 - 10 of 1,817

Connection Between Continuous and Discrete Time Quantum Walks on d-Dimensional Lattices; Extensions to General Graphs

by unknown authors , 2009
"... I obtain the dynamics of the continuous time quantum walk on a d-dimensional lattice, with periodic boundary conditions, as an appropriate limit of the dynamics of the discrete time quantum walk on the same lattice. This extends the main result of [8] which proved this limit for the case of the quan ..."
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I obtain the dynamics of the continuous time quantum walk on a d-dimensional lattice, with periodic boundary conditions, as an appropriate limit of the dynamics of the discrete time quantum walk on the same lattice. This extends the main result of [8] which proved this limit for the case

d '-Dimensional Defect in d-Dimensional Lattice--Nonuniversal Critical Exponents for Long-Range Interactions in the Limit n-+ 00--

by Kazuo Ideura, Ryuzo Abe , 1983
"... Local critical exponent 7J1I in a defect space is investigated up to 0(..12) in the limit n~OO for a system with long-range interactions. It is shown that if d = 315/2 and d ' = 15 critical exponents are nonuniversal but satisfy usual scaling law relations up to 0(..1). ..."
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Local critical exponent 7J1I in a defect space is investigated up to 0(..12) in the limit n~OO for a system with long-range interactions. It is shown that if d = 315/2 and d ' = 15 critical exponents are nonuniversal but satisfy usual scaling law relations up to 0(..1).

Critical and multicritical semi-random (1 + d)dimensional lattices and hard objects in d dimensions

by P. Di Francesco, E. Guitter - J. Phys. A Math. Gen , 2002
"... We investigate models of (1+d)-D Lorentzian semi-random lattices with one random (space-like) direction and d regular (time-like) ones. We prove a general inversion formula expressing the partition function of these models as the inverse of that of hard objects in d dimensions. This allows for an ex ..."
Abstract - Cited by 7 (2 self) - Add to MetaCart
We investigate models of (1+d)-D Lorentzian semi-random lattices with one random (space-like) direction and d regular (time-like) ones. We prove a general inversion formula expressing the partition function of these models as the inverse of that of hard objects in d dimensions. This allows

A monotonicity result for hard-core and Widom-Rowlinson models on certain d-dimensional lattices

by Olle Häggström , 2001
"... For each d 2, we give examples of d-dimensional periodic lattices on which the hard-core and Widom--Rowlinson models exhibit a phase transition which is monotonic, in the sense that there exists a critical value c for the activity parameter , such that there is a unique Gibbs measure (resp. multi ..."
Abstract - Cited by 3 (0 self) - Add to MetaCart
For each d 2, we give examples of d-dimensional periodic lattices on which the hard-core and Widom--Rowlinson models exhibit a phase transition which is monotonic, in the sense that there exists a critical value c for the activity parameter , such that there is a unique Gibbs measure (resp

CSL866: Percolation and Random Graphs Amitabha Bagchi IIT Delhi Scribe: Ayush Nayyar Lecture 2: Introduction to bond percolation and

by Critical Probability , 2007
"... 2.1 Bond percolation: Notation and definitions We now turn our attention to bond percolation in d-dimensional lattices. Let ..."
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2.1 Bond percolation: Notation and definitions We now turn our attention to bond percolation in d-dimensional lattices. Let

Q-Harmonic Oscillator in a Lattice Model

by Hans Van Leeuwen, Hans Maassen
"... We give an explicit proof of the pair partitions formula for the moments of the q-harmonic oscillator, and of the claim made by G. Parisi that the q-deformed lattice Laplacian on the d-dimensional lattice tends to the q-harmonic oscillator in distribution for d !1. 1 ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
We give an explicit proof of the pair partitions formula for the moments of the q-harmonic oscillator, and of the claim made by G. Parisi that the q-deformed lattice Laplacian on the d-dimensional lattice tends to the q-harmonic oscillator in distribution for d !1. 1

Dirac-Connes Operator on Discrete Abelian Groups and Lattices

by Jian Dai, Xing-chang Song , 2001
"... A kind of Dirac-Connes operator defined in the framework of Connes ’ NCG is introduced on discrete abelian groups; it satisfies a Junk-free condition, and bridges the NCG composed by Dimakis, Müller-Hoissen and Sitarz and the NCG of Connes. Then we apply this operator to d-dimensional lattices. ..."
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A kind of Dirac-Connes operator defined in the framework of Connes ’ NCG is introduced on discrete abelian groups; it satisfies a Junk-free condition, and bridges the NCG composed by Dimakis, Müller-Hoissen and Sitarz and the NCG of Connes. Then we apply this operator to d-dimensional lattices.

The Solution of the d-Dimensional Twisted Group Lattices

by Olaf Lechtenfeld, Stuart Samuel , 1994
"... The general d-dimensional twisted group lattice is solved. The irreducible representations of the corresponding group are constructed by an explicit procedure. It is proven that they are complete. All matrix representation The general d-dimensional twisted group lattice is a particular kind of group ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
The general d-dimensional twisted group lattice is solved. The irreducible representations of the corresponding group are constructed by an explicit procedure. It is proven that they are complete. All matrix representation The general d-dimensional twisted group lattice is a particular kind

Norm bounds for Ehrhart polynomial roots

by Benjamin Braun , 2006
"... In 1, M. Beck, J. De Loera, M. Develin, J. Pfeifle and R. Stanley found that the roots of the Ehrhart polynomial of a d-dimensional lattice polytope are bounded above in norm by 1 + (d + 1)!. We provide an improved bound which is quadratic in d and applies to a larger family of polynomials. ..."
Abstract - Cited by 10 (2 self) - Add to MetaCart
In 1, M. Beck, J. De Loera, M. Develin, J. Pfeifle and R. Stanley found that the roots of the Ehrhart polynomial of a d-dimensional lattice polytope are bounded above in norm by 1 + (d + 1)!. We provide an improved bound which is quadratic in d and applies to a larger family of polynomials.

Noncommutative Geometry of Lattice and Staggered Fermions

by Jian Dai, Xing-chang Song , 2000
"... Differential structure of a d-dimensional lattice, which is essentially a noncommutative exterior algebra, is defined using reductions in first order and second order of universal differential calculus in the context of noncommutative geometry(NCG) developed by Dimakis et al. This differential struc ..."
Abstract - Cited by 4 (4 self) - Add to MetaCart
Differential structure of a d-dimensional lattice, which is essentially a noncommutative exterior algebra, is defined using reductions in first order and second order of universal differential calculus in the context of noncommutative geometry(NCG) developed by Dimakis et al. This differential
Results 1 - 10 of 1,817