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Quantum Zeno and Anti-Zeno Effects: An Exact Model
Get PDFRecent studies suggest that both the quantum Zeno (increase of the natural lifetime of an unstable quantum state by repeated measurements) and anti-Zeno (decrease of the natural lifetime) effects can be made manifest in the same system by simply changing the dissipative decay rate associated with the environment. We present an exact calculation confirming this expectation
Non-commutative Complex Projective Spaces and the Standard Model
Get PDFThe standard model fermion spectrum, including a right handed neutrino, can be obtained as a zero-mode of the Dirac operator on a space which is the product of complex projective spaces of complex dimension two and three. The construction requires the introduction of topologically non-trivial background gauge fields. By borrowing from ideas in Connes’ non-commutative geometry and making the complex spaces ‘fuzzy’ a matrix approximation to the fuzzy space allows for three generations to emerge. The generations are associated with three copies of space-time. Higgs’ fields and Yukawa couplings can be accommodated in the usual way
Exact solution of the infinite-range-hopping Bose-Hubbard model
Get PDFThe thermodynamic behaviour of the Bose-Hubbard model is solved for any temperature and any chemical potential. It is found that there is a range of of critical coupling strengths λ_c1 < λ_c2 < λ_c3 < ... in this model. For coupling strengths between λ_c,k and λ_c,(k+1), Bose-Einstein condensation is suppressed at densities near the integer values p = 1, ... , k with an energy gap. This is known as a Mott insulator phase and was previously shown only for zero temperature. In the context of ultra-cold atoms, this phenomenon was experimentally observed in 2002 [1] but, in the Bose-Hubbard model, it manifests itself also in the pressure-volume diagram at high pressures. It is suggested that this phenomenon persists for finite-range hopping and might also be experimentally observable
Supersymmetry in quantum mechanics with point interactions
Get PDFWe investigate supersymmetry in one-dimensional quantum mechanics with point interactions. We clarify a class of point interactions compatible with supersymmetry and present N = 2 supersymmetric models on a circle with two point interactions as well as a superpotential. A hidden su(2) structure inherent in the system plays a crucial role to construct the N = 2 supercharges. Spontaneous supersymmetry breaking due to point interactions and an extension to higher N-extended supersymmetry are also discussed
Localization of fermions to branes: codimension d ≥ 2
Get PDFMotivated by recent experiments, we consider a Schrödinger cat superposition of two widely separated coherent states in thermal equilibrium. The time development of our system is obtained using Wigner distribution functions. In contrast to our discussion for a two-Gaussian wave packet [Phys. Lett. A 286 (2001) 87], we find that, in the absence of dissipation, the interference term does not decay rapidly in time, but in common with the other two terms, it oscillates in time and persists for all times
Random Walks on a Complete Graph: A Model for Infection
Get PDFWe introduce a new model for the infection of one or more subjects by a single agent and calculate the probability of infection after a fixed length of time. We model the agent and subjects as random walkers on a complete graph of N sites, jumping with equal rates from site to site. When one of the walkers is at the same site as the agent for a length of time τ, we assume that the infection probability is given by an exponential law with parameter γ, i.e. q(τ) = 1 − e^(−γτ). We introduce the boundary condition that all walkers return to their initial site (‘home’) at the end of a fixed period T. We also assume that the incubation period is longer than T so that there is no immediate propagation of the infection. In this model, we find that for short periods T, i.e. γT << 1 and T << 1, the infection probability is remarkably small and behaves like T^3. On the other hand, for large T, the probability tends to 1 (as might be expected) exponentially. However, the dominant exponential rate is given approximately by 2γ/((2+γ)N) and is therefore small for large N
Quantization of Bosonic String Model in 26+2-dimensional Spacetime
Get PDFWe investigate the quantization of the bosonic string model which has a local U(1)_V × U(1)_A gauge invariance as well as the general coordinate and Weyl invariance on the world-sheet. The model is quantized by Lagrangian and Hamiltonian BRST formulations á la Batalin, Fradkin and Vilkovisky and noncovariant light-cone gauge formulation. Upon the quantization the model turns out to be formulated consistently in 26+2-dimensional background spacetime involving two time-like coordinates
Probabilistic derivation of a noncommutative version of Varadhan’s Theorem
Get PDFWe give a simple probabilistic derivation of a special case of a noncommutative version of Varadhan’s theorem, first proved by Petz, Raggio and Verbeure. It is based on a Feynman-Kac representation combined with a standard large deviation argument. In the final section, this theorem is then extended to a more difficult situation with Bose-symmetry