1,180 research outputs found
A Quantum Monte Carlo Method at Fixed Energy
In this paper we explore new ways to study the zero temperature limit of
quantum statistical mechanics using Quantum Monte Carlo simulations. We develop
a Quantum Monte Carlo method in which one fixes the ground state energy as a
parameter. The Hamiltonians we consider are of the form
with ground state energy E. For fixed and V, one can view E as a
function of whereas we view as a function of E. We fix E
and define a path integral Quantum Monte Carlo method in which a path makes no
reference to the times (discrete or continuous) at which transitions occur
between states. For fixed E we can determine and other ground
state properties of H
Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms
Let and be two integers with , and let and be
integers with and . In this paper, we prove that , where is a constant depending on and .Comment: 8 pages. To appear in Archiv der Mathemati
Optical mode crossings and the low temperature anomalies of SrTiO3
Optical mode crossing is not a plausible explanation for the new broad
Brillouin doublet nor for the strong acoustic anomalies observed at low
temperatures in SrTiO3. Data presented to support that explanation are also
inconclusive.Comment: This is a comment to a paper from J.F. Scott (same ZFP volume
Integral Difference Ratio Functions on Integers
number theoryInternational audienceTo Jozef, on his 80th birthday, with our gratitude for sharing with us his prophetic vision of Informatique Abstract. Various problems lead to the same class of functions from integers to integers: functions having integral difference ratio, i.e. verifying f (a) − f (b) ≡ 0 (mod (a − b)) for all a > b. In this paper we characterize this class of functions from Z to Z via their a la Newton series expansions on a suitably chosen basis of polynomials (with rational coefficients). We also exhibit an example of such a function which is not polynomial but Bessel like
Correlation functions of the One-Dimensional Random Field Ising Model at Zero Temperature
We consider the one-dimensional random field Ising model, where the spin-spin
coupling, , is ferromagnetic and the external field is chosen to be
with probability and with probability . At zero temperature, we
calculate an exact expression for the correlation length of the quenched
average of the correlation function in the case that is not an integer. The
result is a discontinuous function of . When , we also
place a bound on the correlation length of the quenched average of the
correlation function .Comment: 12 pages (Plain TeX with one PostScript figure appended at end), MIT
CTP #220
The least common multiple of a sequence of products of linear polynomials
Let be the product of several linear polynomials with integer
coefficients. In this paper, we obtain the estimate: as , where is a constant depending on
.Comment: To appear in Acta Mathematica Hungaric
Using Classical Probability To Guarantee Properties of Infinite Quantum Sequences
We consider the product of infinitely many copies of a spin-
system. We construct projection operators on the corresponding nonseparable
Hilbert space which measure whether the outcome of an infinite sequence of
measurements has any specified property. In many cases, product
states are eigenstates of the projections, and therefore the result of
measuring the property is determined. Thus we obtain a nonprobabilistic quantum
analogue to the law of large numbers, the randomness property, and all other
familiar almost-sure theorems of classical probability.Comment: 7 pages in LaTe
Derivation of the Quantum Probability Rule without the Frequency Operator
We present an alternative frequencists' proof of the quantum probability rule
which does not make use of the frequency operator, with expectation that this
can circumvent the recent criticism against the previous proofs which use it.
We also argue that avoiding the frequency operator is not only for technical
merits for doing so but is closely related to what quantum mechanics is all
about from the viewpoint of many-world interpretation.Comment: 12 page
Quantum Energies of Interfaces
We present a method for computing the one-loop, renormalized quantum energies
of symmetrical interfaces of arbitrary dimension and codimension using
elementary scattering data. Internal consistency requires finite-energy sum
rules relating phase shifts to bound state energies.Comment: 8 pages, 1 figure, minor changes, Phys. Rev. Lett., in prin
Grover's algorithm on a Feynman computer
We present an implementation of Grover's algorithm in the framework of
Feynman's cursor model of a quantum computer. The cursor degrees of freedom act
as a quantum clocking mechanism, and allow Grover's algorithm to be performed
using a single, time-independent Hamiltonian. We examine issues of locality and
resource usage in implementing such a Hamiltonian. In the familiar language of
Heisenberg spin-spin coupling, the clocking mechanism appears as an excitation
of a basically linear chain of spins, with occasional controlled jumps that
allow for motion on a planar graph: in this sense our model implements the idea
of "timing" a quantum algorithm using a continuous-time random walk. In this
context we examine some consequences of the entanglement between the states of
the input/output register and the states of the quantum clock
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