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Register a new userAlgebraic approach to multiple defects on the line and application to Casimir force
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An algebraic framework for quantization in presence of arbitrary number of point-like defects on the line is developed. We consider a scalar field which interacts with the defects and freely propagates away of them. As an application we compute the Casimir force both at zero and finite temperature. We derive also the charge density in the Gibbs state of a complex scalar field with defects. The example of two delta-defects is treated in detail.
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The Casimir force between parallel lines in a theory describing condensed vortices in a plane is determined. We make use of the relation between a Chern-Simons-Higgs model and its dualized version, which is expressed in terms of a dual gauge field and a vortex field. The dual model can have a phase of condensed vortices and, in this phase, there is a mapping to a model of two non-interacting massive scalar fields from which the Casimir force can readily be obtained. The choice of boundary conditions required for the mapped scalar fields and their association with those for the vectorial field and the issues involved are discussed. We also briefly discuss the implications of our results for experiments related to the Casimir effect when vortices can be present.
A geometric approach to general quantum statistical systems (including the harmonic oscillator) is presented. It is applied to Casimir energy and the dissipative system with friction. We regard the (N+1)-dimensional Euclidean {it coordinate} system (X$^i$,$tau$) as the quantum statistical system of N quantum (statistical) variables (X$^i$) and one {it Euclidean time} variable ($tau$). Introducing paths (lines or hypersurfaces) in this space (X$^i$,$tau$), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the {it mechanical} system. The system Hamiltonian appears as the {it area}. We show quantization is realized by the {it minimal area principle} in the present geometric approach. When we take a {it line} as the path, the path-integral expressions of the free energy are shown to be the ordinary ones (such as N harmonic oscillators) or their simple variation. When we take a {it hyper-surface} as the path, the system Hamiltonian is given by the {it area} of the {it hyper-surface} which is defined as a {it closed-string configuration} in the bulk space. In this case, the system becomes a O(N) non-linear model. We show the recently-proposed 5 dimensional Casimir energy (ArXiv:0801.3064,0812.1263) is valid. We apply this approach to the visco-elastic system, and present a new method using the path-integral for the calculation of the dissipative properties.
We introduce and formalize the concept of information flux in a many-body register as the influence that the dynamics of a specific element receive from any other element of the register. By quantifying the information flux in a protocol, we can design the most appropriate initial state of the system and, noticeably, the distribution of coupling strengths among the parts of the register itself. The intuitive nature of this tool and its flexibility, which allow for easily manageable numerical approaches when analytic expressions are not straightforward, are greatly useful in interacting many-body systems such as quantum spin chains. We illustrate the use of this concept in quantum cloning and quantum state transfer and we also sketch its extension to non-unitary dynamics.
We comment on the recent work [1], and on its relations with our papers [2,3] cited therein. In particular we show that, contrarily to what stated in [1], the Casimir energy density determined therein in the case of a single delta-like singularity coincides with the energy density obtained previously in our paper [2] using a different approach.
We derive the Casimir force expression from Maxwells stress tensor by means of original quantum-electro-dynamical cavity modes. In contrast with similar calculations, our method is straightforward and does not rely on intricate mathematical extrapolation relations.
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