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1,817
Connection Between Continuous and Discrete Time Quantum Walks on dDimensional Lattices; Extensions to General Graphs
, 2009
"... I obtain the dynamics of the continuous time quantum walk on a ddimensional 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 ddimensional 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 dDimensional LatticeNonuniversal Critical Exponents for LongRange Interactions in the Limit n+ 00
, 1983
"... Local critical exponent 7J1I in a defect space is investigated up to 0(..12) in the limit n~OO for a system with longrange 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 longrange 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 semirandom (1 + d)dimensional lattices and hard objects in d dimensions
 J. Phys. A Math. Gen
, 2002
"... We investigate models of (1+d)D Lorentzian semirandom lattices with one random (spacelike) direction and d regular (timelike) 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 ..."
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Cited by 7 (2 self)
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We investigate models of (1+d)D Lorentzian semirandom lattices with one random (spacelike) direction and d regular (timelike) 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 hardcore and WidomRowlinson models on certain ddimensional lattices
, 2001
"... For each d 2, we give examples of ddimensional periodic lattices on which the hardcore and WidomRowlinson 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 ..."
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Cited by 3 (0 self)
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For each d 2, we give examples of ddimensional periodic lattices on which the hardcore and WidomRowlinson 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
, 2007
"... 2.1 Bond percolation: Notation and definitions We now turn our attention to bond percolation in ddimensional lattices. Let ..."
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2.1 Bond percolation: Notation and definitions We now turn our attention to bond percolation in ddimensional lattices. Let
QHarmonic Oscillator in a Lattice Model
"... We give an explicit proof of the pair partitions formula for the moments of the qharmonic oscillator, and of the claim made by G. Parisi that the qdeformed lattice Laplacian on the ddimensional lattice tends to the qharmonic oscillator in distribution for d !1. 1 ..."
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Cited by 1 (0 self)
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We give an explicit proof of the pair partitions formula for the moments of the qharmonic oscillator, and of the claim made by G. Parisi that the qdeformed lattice Laplacian on the ddimensional lattice tends to the qharmonic oscillator in distribution for d !1. 1
DiracConnes Operator on Discrete Abelian Groups and Lattices
, 2001
"... A kind of DiracConnes operator defined in the framework of Connes ’ NCG is introduced on discrete abelian groups; it satisfies a Junkfree condition, and bridges the NCG composed by Dimakis, MüllerHoissen and Sitarz and the NCG of Connes. Then we apply this operator to ddimensional lattices. ..."
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A kind of DiracConnes operator defined in the framework of Connes ’ NCG is introduced on discrete abelian groups; it satisfies a Junkfree condition, and bridges the NCG composed by Dimakis, MüllerHoissen and Sitarz and the NCG of Connes. Then we apply this operator to ddimensional lattices.
The Solution of the dDimensional Twisted Group Lattices
, 1994
"... The general ddimensional 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 ddimensional twisted group lattice is a particular kind of group ..."
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Cited by 1 (0 self)
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The general ddimensional 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 ddimensional twisted group lattice is a particular kind
Norm bounds for Ehrhart polynomial roots
, 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 ddimensional 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. ..."
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Cited by 10 (2 self)
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In 1, M. Beck, J. De Loera, M. Develin, J. Pfeifle and R. Stanley found that the roots of the Ehrhart polynomial of a ddimensional 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
, 2000
"... Differential structure of a ddimensional 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 ..."
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Cited by 4 (4 self)
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Differential structure of a ddimensional 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
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1,817