The theory of adiabatic invariants has a long history, and very important implications and applications in many different branches of physics, classically and quantally, but is rarely founded on rigorous results. Here we treat the general timedependent one-dimensional harmonic oscillator, whose Newton equation q̈+ω(t)q = 0 cannot be solved in general. We follow the time-evolution of an initial e...

We show the set of faithful representations of a closed orientable hyperbolic surface group is dense in both irreducible components of the PSL2(K) representation variety, where K = C or R, answering a question of W. Goldman. We also prove the existence of faithful representations into PU(2, 1) with certain nonintegral Toledo invariants.

The crepant resolution conjecture states that the Gromov–Witten invariants of an orbifold X should be determined in a precise way by the Gromov–Witten invariants of a crepant resolution of its coarse moduli space. We compute the Gromov–Witten invariants of the stack symmetric square of P 2 and compare them with the Gromov– Witten invariants of its crepant resolution, Hilb 2 P 2 (which were comp...

This work aims to study a Stirling engine (SE) used recover the heat content of exhaust gas from an internal combustion engine. The attention has been focused on transfer between and working inside heater. Experimental tests have performed two-cylinder gamma-type coupled compression ignition using thermally insulated pipe cap. A mechanical power 0.275 kW at 900 rpm SE rotational speed was obtai...

Abstract The efficiency of small thermal machines is typically a fluctuating quantity. We here study the large deviation properties two exemplary quantum heat engines, harmonic oscillator and two-level Otto motors. To this end, we analytically compute their joint characteristic functions for work based on two-projective-measurement approach. investigate work–heat correlations within respective ...