arXiv subjects

Shin Takagi

Publications and source records attributed to Shin Takagi.

3 recordsLinked to original sources

arXiv2001

Method of Collective Degrees of Freedom in Spin Coherent State Path Integral

We present a detailed field theoretic description of those collective degrees of freedom (CDF) which are relevant to study macroscopic quantum dynamics of a quasi-one-dimensional ferromagnetic domain wall. We apply spin coherent state path integral (SCSPI) in the proper discrete time formalism (a) to extract the relevant CDF's, namely, the center position and the chirality of the domain wall, which originate from the translation and the rotation invariances of the system in question, and (b) to derive effective action for the CDF's by elimination of environmental zero-modes with the help of the {\it Faddeev-Popov technique}. The resulting effective action turns out to be such that both the center position and the chirality can be formally described by boson coherent state path integral. However, this is only formal; there is a subtle departure from the latter.

cond-mat.mes-hall↗

arXiv1999

Macroscopic Quantum Dynamics of a Free Domain Wall in a Ferromagnet

We study macroscopic quantum dynamics of a free domain wall in a quasi-one-dimensional ferromagnet by use of the spin-coherent-state path integral in {\it discrete-time} formalism. Transition amplitudes between typical states are quantitatively discussed by use of {\it stationary-action approximation} with respect to collective degrees of freedom representing the center position and the chirality of the domain wall. It is shown that the chirality may be loosely said to be canonically conjugate to the center position; the latter moves with a speed depending on the former. It is clarified under what condition the center position can be regarded as an effective free-particle position, which exhibits the phenomenon of wave-packet spreading. We demonstrate, however, that in some case the non-linear character of the spin leads to such a dramatic phenomenon of a non-spreading wave packet as to completely invalidate the free-particle analogy. In the course of the discussion, we also point out various difficulties associated with the continuous-time formalism.

cond-mat.mes-hall↗

arXiv1998

A Note on (Spin-) Coherent-State Path Integral

It is pointed out that there are some fundamental difficulties with the frequently used continuous-time formalism of the spin-coherent-state path integral. They arise already in a single-spin system and at the level of the "classical action" not to speak of fluctuations around the "classical path". Similar difficulties turn out to be present in the case of the (boson-)coherent-state path integral as well; although partially circumventable by an ingenious trick (Klauder's $ε$-prescription) at the "classical level", they manifest themselves at the level of fluctuations. Detailed analysis of the origin of these difficulties makes it clear that the only way of avoiding them is to work with the proper discrete-time formalism. The thesis is explicitly illustrated with a harmonic oscillator and a spin under a constant magnetic field.

quant-ph↗