Quantum Fokker-Planck Master Equation for Continuous Feedback Control.

Measurement and feedback control are essential features of quantum science, with applications ranging from quantum technology protocols to information-to-work conversion in quantum thermodynamics. Theoretical descriptions of feedback control are typically given in terms of stochastic equations requiring numerical solutions, or are limited to linear feedback protocols. Here we present a formalism for continuous quantum measurement and feedback, both linear and nonlinear. Our main result is a quantum Fokker-Planck master equation describing the joint dynamics of a quantum system and a detector with finite bandwidth. For fast measurements, we derive a Markovian master equation for the system alone, amenable to analytical treatment. We illustrate our formalism by investigating two basic information engines, one quantum and one classical.

From a feedback-controlled demon to an information ratchet in a double quantum dot.

We present a simple strategy for constructing an information ratchet or memory-tape model of Maxwell's demon, from a feedback-controlled model. We illustrate our approach by converting the Annby-Andersson feedback-controlled double quantum dot model [Phys. Rev. B 101, 165404 (2020)2469-995010.1103/PhysRevB.101.165404] to a memory-tape model. We use the underlying network structure of the original model to design a set of bit interaction rules for the information ratchet. The new model is solved analytically in the limit of long interaction times. For finite-time interactions, semianalytical phase diagrams of operational modes are obtained. Stochastic simulations are used to verify theoretical results.

Clusterization of self-propelled particles in a two-component system.

We consider a mixture of active solute molecules in a suspension of passive solvent particles comprising a thermal bath. The solute molecules are considered to be extended objects with two chemically distinct heads, one head of which having chemical affinity towards the solvent particles. The coupled Langevin equations for the solvent particles along with the equations governing the dynamics of active molecules are numerically simulated to show how the active molecules self-assemble to form clusters which remain in dynamic equilibrium with the free solute molecules. We observe an interesting crossover at an intermediate time in the variation of the order parameter with time when the temperature of the bath is changed signifying the differential behavior of clusterization below and above the crossover time associated with a transition between a thermodynamic and a quasithermodynamic regime. Enthalpy-entropy compensation in the formation of clusters below the crossover is demonstrated.

Brownian dynamics of self-regulated particles with additional degrees of freedom: Symmetry breaking and homochirality.

We consider the Brownian motion of a collection of particles each with an additional degree of freedom. The degree of freedom of a particle (or, in general, a molecule) can assume distinct values corresponding to certain states or conformations. The time evolution of the additional degree of freedom of a particle is guided by those of its neighbors as well as the temperature of the system. We show that the local averaging over these degrees of freedom results in emergence of a collective order in the dynamics in the form of selection or dominance of one of the isomers leading to a symmetry-broken state. Our statistical model captures the basic features of homochirality, e.g., autocatalysis and chiral inhibition.

Prebiotic Chemistry of HCN Tetramerization by Automated Reaction Search.

HCN oligomerization is considered to be one of the important pathways in chemical evolution. Nucleobases, aminoacids, and many other complex organic molecules can evolve through this pathway. We report an explorative study based on an automated reaction search method that avoids the cognitive bias present when searching chemical reaction space. We discuss the chemical space of the HCN dimer in detail, and the important trimers and tetramers are discussed briefly. A component-wise molecular-fingerprint-based methodology is proposed to identify molecular similarity. We present four different thermal routes to cis/trans-2,3-diaminomaleonitrile and 4-amino-1H-imidazole-5-carbonitrile, which are important intermediates in prebiotic chemistry.