Related papers: Limitations of Self-Assembly at Temperature One (e…
It is argued that self-duality of one system leads to the zero finite-size scaling amplitude of the critical internal energy for all system belonging to the same universality class. For such models, we may expect that condition of equality…
Silicon self-assembly at step edges in the initial stage of homoepitaxial growth on a vicinal Si(111) surface is studied by scanning tunneling microscopy (STM). The resulting atomic structures change dramatically from a parallel array of…
In finite-dimensional quantum systems, temperature cannot be uniquely defined. This, in turn, implies that there are several ways to define entropy production in finite-dimensional quantum systems, because the classical entropy production…
The configurational entropy is among the key observables to characterize experimentally the formation of a glass. Physically, it quantifies the multiplicity of metastable states in which an amorphous material can be found at a given…
Controlling the topology of structures self-assembled from a set of heterogeneous building blocks is highly desirable for many applications, but is poorly understood theoretically. Here we show that the thermodynamic theory of self-assembly…
The trace of the heat kernel in a (D+1)-dimensional Euclidean spacetime (integer D > 1) is used to derive the free energy in finite temperature field theory. The spacetime presents a D-dimensional compact space (domain) with a…
Quantum annealers are emerging as programmable, dynamical experimental platforms for probing strongly correlated spin systems. Yet key thermal assumptions, chiefly a Gibbs-distributed output ensemble, remain unverified in the large-scale…
A visceral structure on M is given by a definable base for a uniform topology on its universe in which all basic open sets are infinite and any infinite definable subset X of M has non-empty interior. This context includes o-minimal ordered…
Experiments have reached a monumental capacity for designing and synthesizing microscopic particles for self-assembly, making it possible to precisely control particle concentrations, shapes, and interactions. However, more physical insight…
In earlier work, the author described various stratification conditions for a complex analytic set X in terms of the theory of integral closure of modules. However, even if an analytic set has a reduced structure, often geometric operations…
A challenge of molecular self-assembly is to understand how to design particles that self-assemble into a desired structure and not any of a potentially large number of undesired structures. Here we use simulation to show that a strategy of…
The purpose of these notes is to give a fairly narrow but thorough introduction to the spectral analysis of Hamiltonians and standard Liouvilleans describing finite dimensional small systems linearly coupled to a scalar massless field or…
We investigate how the temperature calculated from the microcanonical entropy compares with the canonical temperature for finite isolated quantum systems. We concentrate on systems with sizes that make them accessible to numerical exact…
Calculations of the thermodynamical properties of a supercooled liquid confined in a matrix are performed with an inherent structure analysis. The liquid entropy is computed by means of a thermodynamical integration procedure. The…
A pair of two-level systems initially prepared in different thermal states and coupled to an external reversible work source, do not in general reach a common temperature at the end of a unitary work extraction process. We define an…
Self-assembly of granular particles is of great interest in both applied and basic research. It is commonly observed that when randomly packed into a container, granular particles form disordered structures like glass. As the particles are…
An estimator for the dynamical temperature in an arbitrary ensemble is derived in the framework of Bayesian statistical mechanics and the maximum entropy principle. We test this estimator numerically by a simulation of the two-dimensional…
We formulate a mixed-state analog of the NLTS conjecture [FH14] by asking whether there exist topologically-ordered systems for which the thermal Gibbs state for constant temperature is globally-entangled in the sense that it cannot even be…
We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are…
A computable structure $\mathcal{A}$ is decidable if, given a formula $\varphi(\bar{x})$ of elementary first-order logic, and a tuple $\bar{a} \in \mathcal{A}$, we have a decision procedure to decide whether $\varphi$ holds of $\bar{a}$. We…