4,423 research outputs found

### Quantum Corrections to Q-Balls

We extend calculational techniques for static solitons to the case of field
configurations with simple time dependence in order to consider quantum effects
on the stability of Q-balls. These nontopological solitons exist classically
for any fixed value of an unbroken global charge Q. We show that one-loop
quantum effects can destabilize very small Q-balls. We show how the properties
of the soliton are reflected in the associated scattering problem, and find
that a good approximation to the full one-loop quantum energy of a Q-ball is
given by $\omega - E_0$, where $\omega$ is the frequency of the classical
soliton's time dependence, and $E_0$ is the energy of the lowest bound state in
the associated scattering problem.Comment: 6 pages, 2 figures, uses RevTex4; v2: replaced figure

### Upper bounds for the order of an additive basis obtained by removing a finite subset of a given basis

Let $A$ be an additive basis of order $h$ and $X$ be a finite nonempty subset
of $A$ such that the set $A \setminus X$ is still a basis. In this article, we
give several upper bounds for the order of $A \setminus X$ in function of the
order $h$ of $A$ and some parameters related to $X$ and $A$. If the parameter
in question is the cardinality of $X$, Nathanson and Nash already obtained some
of such upper bounds, which can be seen as polynomials in $h$ with degree $(|X|
+ 1)$. Here, by taking instead of the cardinality of $X$ the parameter defined
by d := \frac{\diam(X)}{\gcd\{x - y | x, y \in X\}}, we show that the order
of $A \setminus X$ is bounded above by $(\frac{h (h + 3)}{2} + d \frac{h (h -
1) (h + 4)}{6})$. As a consequence, we deduce that if $X$ is an arithmetic
progression of length $\geq 3$, then the upper bounds of Nathanson and Nash are
considerably improved. Further, by considering more complex parameters related
to both $X$ and $A$, we get upper bounds which are polynomials in $h$ with
degree only 2.Comment: 17 page

### 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 $H=H_{0}+\lambda V$
with ground state energy E. For fixed $H_{0}$ and V, one can view E as a
function of $\lambda$ whereas we view $\lambda$ 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 $\lambda(E)$ and other ground
state properties of H

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