相关论文: The Jones polynomial in systems with Periodic Boun…

Knots, links and entangled filaments appear in many physical systems of interest in biology and engineering. Classifying knots and measuring entanglement is of interest both for advancing knot theory, as well as for analyzing large data…

Measuring the entanglement complexity of collections of open curves in 3-space has been an intractable, yet pressing mathematical problem, relevant to a plethora of physical systems, such as in polymers and biopolymers. In this manuscript,…

Circuit topology employs fundamental units of entanglement, known as soft contacts, for constructing knots from the bottom up, utilising circuit topology relations, namely parallel, series, cross, and concerted relations. In this article,…

This thesis details a Python-based software designed to calculate the Jones polynomial, a vital mathematical tool from Knot Theory used for characterizing the topological and geometrical complexity of curves in \( \mathbb{R}^3 \), which is…

Many structures in science, engineering, and art can be viewed as curves in 3-space. The entanglement of these curves plays a crucial role in determining the functionality and physical properties of materials. Many concepts in knot theory…

We use Brownian dynamics simulations and advanced topological profiling methods to characterize the out-of-equilibrium evolution of self-entanglement in linear polymers confined into nano-channels and under periodic compression. We…

Projected Entangled Pair States (PEPS) are recognized as a potent tool for exploring two-dimensional quantum many-body systems. However, a significant challenge emerges when applying conventional PEPS methodologies to systems with periodic…

This paper will be an exposition of the Kauffman bracket polynomial model of the Jones polynomial, tangle methods for computing the Jones polynomial, and the use of these methods to produce non-trivial links that cannot be detected by the…

Topological constraints (TCs) between polymers determine the behaviour of complex fluids such as creams, oils and plastics. Most of the polymer solutions used every day life employ linear chains; their behaviour is accurately captured by…

In this manuscript we introduce a method to measure entanglement of curves in 3-space that extends the notion of knot and link polynomials to open curves. We define the bracket polynomial of curves in 3-space and show that it has real…

Using a simple recurrence relation we give a new method to compute Jones polynomials of closed braids: we find a general expansion formula and a rational generating function for Jones polynomials. The method is used to estimate degree of…

We examine the structure and dimensionality of the Jones polynomial using manifold learning techniques. Our data set consists of more than 10 million knots up to 17 crossings and two other special families up to 2001 crossings. We introduce…

Polymer rings in solution are either permanently entangled or not. Permanent topological restrictions give rise to additional entropic interactions apart from the ones arising due to mere chain flexibility or excluded volume. Conversely,…

We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can…

Continuous variables systems find valuable applications in quantum information processing. To deal with an infinite-dimensional Hilbert space, one in general has to handle large numbers of discretized measurements in tasks such as…

The introduction of the infinite boundary terms and the pairwise interactions [J. Chem. Theory Comput., 10, 5254, (2014)] enables a physically intuitive approach for deriving electrostatic energy and pressure for both neutral and…

We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single…

In computational models of particle packings with periodic boundary conditions, it is assumed that the packing is attached to exact copies of itself in all possible directions. The periodicity of the boundary then requires that all of the…

We define the local periodic linking number, LK, between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions. The properties of LK indicate that it is an appropriate measure of entanglement…

These two accompanying papers treat two mode entanglement for systems of identical massive bosons and the relationship to spin squeezing and other quantum correlation effects. Entanglement is a key quantum feature of composite systems where…