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A $D$-dimensional Markovian open quantum system will undergo quantum jumps between pure states, if we can monitor the bath to which it is coupled with sufficient precision. In general these jumps, plus the between-jump evolution, create a trajectory which passes through infinitely many different pure states. Here we show that, for any ergodic master equation, one can expect to find an {em adaptive} monitoring scheme on the bath that can confine the system state to jumping between only $K$ states, for some $K geq (D-1)^2+1$. For $D=2$ we explicitly construct a 2-state ensemble for any ergodic master equation, showing that one bit is always sufficient to track a qubit.
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We consider the effect of introducing a small number of non-aligning agents in a well-formed flock. To this end, we modify a minimal model of active Brownian particles with purely repulsive (excluded volume) forces to introduce an alignment interaction that will be experienced by all the particles except for a small minority of dissenters. We find that even a very small fraction of dissenters disrupts the flocking state. Strikingly, these motile dissenters are much more effective than an equal number of static obstacles in breaking up the flock. For the studied system sizes we obtain clear evidence of scale invariance at the flocking-disorder transition point and the system can be effectively described with a finite-size scaling formalism. We develop a continuum model for the system which reveals that dissenters act like annealed noise on aligners, with a noise strength that grows with the persistence of the dissenters dynamics.
Quantum optics did not, and could not, flourish without the laser. The present paper is not about the principles of laser construction, still less a history of how the laser was invented. Rather, it addresses the question: what are the fundamental features that distinguish laser light from thermal light? The obvious answer, laser light is coherent, is, I argue, so vague that it must be put aside at the start, albeit to revisit later. A more specific, quantum theoretic, version, laser light is in a coherent state, is simply wrong in this context: both laser light and thermal light can equally well be described by coherent states, with amplitudes that vary stochastically in space. Instead, my answer to the titular question is that four principles are needed: high directionality, monochromaticity, high brightness, and stable intensity. Combining the first three of these principles suffices to show, in a quantitative way --- involving, indeed, very large dimensionless quantities (up to $sim10^{51}$) --- that a laser must be constructed very differently from a light bulb. This quantitative analysis is quite simple, and is easily relatable to coherence, yet is not to be found in any text-books on quantum optics to my knowledge. The fourth principle is the most subtle and, perhaps surprisingly, is the only one related to coherent states in the quantum optics sense: it implies that the description in terms of coherent states is the only simple description of a laser beam. Interestingly, this leads to the (not, as it turns out, entirely new) prediction that narrowly filtered laser beams are indistinguishable from similarly filtered thermal beams. I hope that other educators find this material useful, it may contain surprises even for researchers who have been in the field longer than I have.
In his Comment, Elsasser claims that the answer to my titular question is one, not four as I have it. He goes on to give the singular principle that supposedly captures the difference between a light-bulb and a laser: $g^{(2)}(tau=0)=1$. His claim is unconsidered and wrong, his proposed principle is impossible to apply and, when corrected, redundant (it then becomes one of the four I list already), his arguments are manifestly misdirected. My paper stands as is.
We present the first numerical simulations that self-consistently follow the formation of dense molecular clouds in colliding flows. Our calculations include a time-dependent model for the H2 and CO chemistry that runs alongside a detailed treatment of the dominant heating and cooling processes in the ISM. We adopt initial conditions characteristic of the warm neutral medium and study two different flow velocities - a slow flow with v = 6.8 km/s and a fast flow with v = 13.6 km/s. The clouds formed by the collision of these flows form stars, with star formation beginning after 16 Myr in the case of the slower flow, but after only 4.4 Myr in the case of the faster flow. In both flows, the formation of CO-dominated regions occurs only around 2 Myr before the onset of star formation. Prior to this, the clouds produce very little emission in the J = 1 -> 0 transition line of CO, and would probably not be identified as molecular clouds in observational surveys. In contrast, our models show that H2-dominated regions can form much earlier, with the timing depending on the details of the flow. In the case of the slow flow, small pockets of gas become fully molecular around 10 Myr before star formation begins, while in the fast flow, the first H2-dominated regions occur around 3 Myr before the first prestellar cores form. Our results are consistent with models of molecular cloud formation in which the clouds are dominated by dark molecular gas for a considerable proportion of their assembly history.
We study transient effects in a setup, where the quantum dot (QD) is abruptly sandwiched between the metallic and superconducting leads. Focusing on the proximity-induced electron pairing, manifested by the in-gap bound states, we determine characteristic time-scale needed for these quasiparticles to develop. In particular, we derive analytic expressions for (i) charge occupancy of the QD, (ii) amplitude of the induced electron pairing, and (iii) the transient currents under equilibrium and nonequilibrium conditions. We also investigate the correlation effects within the Hartree-Fock-Bogolubov approximation, revealing a competition between the Coulomb interactions and electron pairing.
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