Anupam Garg

The semiclassical propagator for spin coherent states

We use a continuous-time path integral to obtain the semiclassical propagator for minimal-spread spin coherent states. We pay particular attention to the “extra phase” discovered by Solari and Kochetov, and show that this correction is related to an anomaly in the fluctuation determinant. We show that, once this extra factor is included, the semiclassical propagator has the correct short time behavior to O(T2), and demonstrate its consistency under dissection of the path.

Tunnel splittings for one-dimensional potential wells revisited

The Wentzel–Kramers–Brillouin and instanton answers for the tunnel splitting of the ground state in a symmetric double-well potential are both reduced to an expression involving only functionals of the potential, without the need for solving any auxilliary problems. This formula is applied to simple model problems. The prefactor for the splitting in the textbook by Landau and Lifshitz is amended so as to apply to the ground and low lying excited states.

Macroscopic Quantum Tunneling

Macroscopic quantum phenomena are particularly important when considering the problem of Schrödinger’s cat. This book contains a coherent and self-contained account of such phenomena, focusing on the central role played by macroscopic quantum tunneling. Beginning with an explanation of the nature and significance of the cat problem, Shin Takagi introduces the concept of macroscopic quantum tunneling. He deals with typical examples in detail, elucidating how quantum mechanical coherence may be lost (so-called ‘decoherence’) or how it may be maintained despite the effects of environment and measurement processes. Recent experimental and theoretical advances are discussed, and the remaining problems described. The final chapter describes an experiment to decide between quantum mechanics and macrorealism in the light of Einstein’s moon. Assumingonly aknowledgeof elementaryquantummechanics, this bookemphasizes conceptual aspects rather than technical details. It provides a firm introduction to the subject for graduate students and researchers.

Semiclassical coherent-state propagator for many particles

We obtain the semiclassical coherent-state propagator for a many-particle system with an arbitrary Hamiltonian.

Spin tunneling in magnetic molecules: Quasisingular perturbations and discontinuous SU(2) instantons

Spin coherent state path integrals with discontinuous semiclassical paths are investigated with special reference to a realistic model for the magnetic degrees of freedom in the

Spin coherent-state path integrals and the instanton calculus

{\mathrm{Fe}}_{8}

Diabolical points in magnetic molecules: An exactly solvable model

molecular solid. It is shown that such paths are essential to a proper understanding of the phenomenon of quenched spin tunneling in these molecules. In the

Oscillatory tunnel splittings in spin systems: A discrete wentzel-kramers-brillouin approach

{\mathrm{Fe}}_{8}

Application of the discrete Wentzel–Kramers–Brillouin method to spin tunneling

problem, such paths are shown to arise as soon as a fourth-order anisotropy term in the energy is turned on, making this term a singular perturbation from the semiclassical point of view. The instanton approximation is shown to quantitatively explain the magnetic field dependence of the tunnel splitting, as well as agree with general rules for the number of quenching points allowed for a given value of spin. A fairly accurate approximate formula for the spacing between quenching points is derived.

Dissipation in macroscopic quantum tunneling and coherence in magnetic particles (invited)

We use an instanton approximation to the continuous-time spin coherent-state path integral to obtain the tunnel splitting of classically degenerate ground states. We show that provided the fluctuation determinant is carefully evaluated, the path integral expression is accurate to order O(1/j). We apply the method to the LMG model and to the molecular magnet Fe8 in a transverse field.