4,423 research outputs found

    Quantum Corrections to Q-Balls

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    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 ωE0\omega - E_0, where ω\omega is the frequency of the classical soliton's time dependence, and E0E_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

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    Let AA be an additive basis of order hh and XX be a finite nonempty subset of AA such that the set AXA \setminus X is still a basis. In this article, we give several upper bounds for the order of AXA \setminus X in function of the order hh of AA and some parameters related to XX and AA. If the parameter in question is the cardinality of XX, Nathanson and Nash already obtained some of such upper bounds, which can be seen as polynomials in hh with degree (X+1)(|X| + 1). Here, by taking instead of the cardinality of XX the parameter defined by d := \frac{\diam(X)}{\gcd\{x - y | x, y \in X\}}, we show that the order of AXA \setminus X is bounded above by (h(h+3)2+dh(h1)(h+4)6)(\frac{h (h + 3)}{2} + d \frac{h (h - 1) (h + 4)}{6}). As a consequence, we deduce that if XX is an arithmetic progression of length 3\geq 3, then the upper bounds of Nathanson and Nash are considerably improved. Further, by considering more complex parameters related to both XX and AA, we get upper bounds which are polynomials in hh with degree only 2.Comment: 17 page

    A Quantum Monte Carlo Method at Fixed Energy

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    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=H0+λVH=H_{0}+\lambda V with ground state energy E. For fixed H0H_{0} and V, one can view E as a function of λ\lambda whereas we view λ\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 λ(E)\lambda(E) and other ground state properties of H
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