arXiv subjects

Antti J. Niemi

Publications and source records attributed to Antti J. Niemi.

At least 19 recordsLinked to original sources

arXiv2026

Fold Catastrophes in a Hopf Texture Driven by a Navier--Stokes Blow-Up Analog

A two-component Bose--Einstein condensate can host a pseudospin Hopf texture coupled to the viscous normal flow of its thermal cloud. Motivated by OpenAI's reported finite-time Navier--Stokes singular solution, we evolve such a texture in a smooth flow reproducing the geometry and similarity scaling of the collapsing axisymmetric core. The evolution creates and annihilates preimage pairs while preserving the Hopf charge. The first one-to-three transition exhibits the square-root opening characteristic of a Thom $A_2$ fold. A subsequent three-to-five transition precedes a burst-like regime of recurrent fold catastrophes and near-caustic activity.

cond-mat.quant-gas↗

arXiv2026

Geometric Qubits in Programmable Atomic Trimers

Motivated by programmable tweezer arrays, we develop an exactly solvable shape-space theory for near-equilateral atomic trimers. The Higgs oscillator on Kendall's shape sphere gives a nonresonant spectral lattice whose fixed-angular-momentum relative-stationary minimizers are supported on two adjacent admissible sites. These symmetry-selected doublets are separated from higher relative-stationary branches by a finite branch gap. With phase-coherent shape-mode driving and Rydberg-mediated conditional phases, they furnish a candidate route to geometric qubits and entangling operations.

quant-ph↗

arXiv2024

Local topology and perestroikas in protein structure and folding dynamics

Methods of local topology are introduced to the field of protein physics. This is achieved by explaining how the folding and unfolding processes of a globular protein alter the local topology of the protein's C-alpha backbone through conformational bifurcations. The mathematical formulation builds on the concept of Arnol'd's perestroikas, by extending it to piecewise linear chains using the discrete Frenet frame formalism. In the low-temperature folded phase, the backbone geometry generalizes the concept of a Peano curve, with its modular building blocks modeled by soliton solutions of a discretized nonlinear Schroedinger equation. The onset of thermal unfolding begins when perestroikas change the flattening and branch points that determine the centers of solitons. When temperature increases, the perestroikas cascade, which leads to a progressive disintegration of the modular structures. The folding and unfolding processes are quantitatively characterized by a correlation function that describes the evolution of perestroikas under temperature changes. The approach provides a comprehensive framework for understanding the Physics of protein folding and unfolding transitions, contributing to the broader field of protein structure and dynamics.

physics.bio-ph↗

arXiv2023

From Feynman's ratchet to timecrystalline molecular motors

Cats use the connection governing parallel transport in the space of shapes to land safely on their feet. Here we argue that this connection also explains the impressive performance of molecular motors by enabling molecules to evade conclusions of Feynman's ratchet-and-pawl analysis. We first demonstrate, using simple molecular models, how directed rotational motion can emerge from shape changes even without angular momentum. We then computationally design knotted polyalanine molecules and show how their shape space connection organizes individual atom thermal vibrations into collective rotational motion, independently of angular momentum. Our simulations show that rotational motion arises effortlessly even in ambient water, making the molecule an effective theory time crystal. Our findings have potential for practical molecular motor design and engineering and can be verified through high-precision nuclear magnetic resonance measurements.

cond-mat.soft↗

arXiv2022

Poincaré index formula and analogy with the Kosterlitz-Thouless transition in a non-rotated cold atom Bose-Einstein condensate

A dilute gas of Bose-Einstein condensed atoms in a non-rotated and axially symmetric harmonic trap is modelled by the time dependent Gross-Pitaevskii equation. When the angular momentum carried by the condensate does not vanish, the minimum energy state describes vortices (or antivortices) that propagate around the trap center. The number of (anti)vortices increases with the angular momentum, and they repel each other to form Abrikosov lattices. Besides vortices and antivortices there are also stagnation points where the superflow vanishes; to our knowledge the stagnation points have not been analyzed previously, in the context of the Gross-Pitaevskii equation. The Poincaré index formula states that the difference in the number of vortices and stagnation points can never change. When the number of stagnation points is small, they tend to aggregate into degenerate propagating structures. But when the number becomes sufficiently large, the stagnation points tend to pair up with the vortex cores, to propagate around the trap center in regular lattice arrangements. There is an analogy with the geometry of the Kosterlitz-Thouless transition, with the angular momentum of the condensate as the external control parameter instead of the temperature.

cond-mat.quant-gas↗

arXiv2021

Time crystals: From Schrödinger to Sisyphus

A Hamiltonian time crystal can emerge when a Noether symmetry is subject to a condition that prevents the energy minimum from being a critical point of the Hamiltonian. A somewhat trivial example is the Schrödinger equation of a harmonic oscillator. The Noether charge for its particle number coincides with the square norm of the wave function, and the energy eigenvalue is a Lagrange multiplier for the condition that the wave function is properly normalized. A more elaborate example is the Gross-Pitaevskii equation that models vortices in a cold atom Bose-Einstein condensate. In an oblate, essentially two dimensional harmonic trap the energy minimum is a topologically protected timecrystalline vortex that rotates around the trap center. Additional examples are constructed using coarse grained Hamiltonian models of closed molecular chains. When knotted, the topology of a chain can support a time crystal. As a physical example, high precision all-atom molecular dynamics is used to analyze an isolated cyclopropane molecule. The simulation reveals that the molecular D$_{3h}$ symmetry becomes spontaneously broken. When the molecule is observed with sufficiently long stroboscopic time steps it appears to rotate like a simple Hamiltonian time crystal. When the length of the stroboscopic time step is decreased the rotational motion becomes increasingly ratcheting and eventually it resembles the back-and-forth oscillations of Sisyphus dynamics. The stroboscopic rotation is entirely due to atomic level oscillatory shape changes, so that cyclopropane is an example of a molecule that can rotate without angular momentum. Finally, the article is concluded with a personal recollection how Frank's and Betsy's Stockholm journey started.

cond-mat.other↗

arXiv2021

Vortex precession and exchange in a Bose-Einstein condensate

Vortices in a Bose-Einstein condensate are modelled as spontaneously symmetry breaking minimum energy solutions of the time dependent Gross-Pitaevskii equation, using the method of constrained optimization. In a non-rotating axially symmetric trap, the core of a single vortex precesses around the trap center and, at the same time, the phase of its wave function shifts at a constant rate. The precession velocity, the speed of phase shift, and the distance between the vortex core and the trap center, depend continuously on the value of the conserved angular momentum that is carried by the entire condensate. In the case of a symmetric pair of identical vortices, the precession engages an emergent gauge field in their relative coordinate, with a flux that is equal to the ratio between the precession and shift velocities.

cond-mat.quant-gas↗

arXiv2020

Rotation by shape change, autonomous molecular motors and effective timecrystalline dynamics

A deformable body can rotate even with no angular momentum, simply by changing its shape. A good example is a falling cat, how it maneuvers in air to land on its feet. Here a first principles molecular level example of the phenomenon is presented. For this the thermal vibrations of individual atoms in an isolated cyclopropane molecule are simulated in vacuum and at ultralow internal temperature values, and the ensuing molecular motion is followed stroboscopically. It is observed that in the limit of long stroboscopic time steps the vibrations combine into an apparent uniform rotation of the entire molecule even in the absence of angular momentum. This large time scale rotational motion is then modeled in an effective theory approach, in terms of timecrystalline Hamiltonian dynamics. The phenomenon is a temperature sensitive measurable. As such it has potential applications that range from models of autonomous molecular motors to development of molecular level detector, sensor and control technologies.

physics.comp-ph↗

arXiv2020

Classical Hamiltonian Time Crystals -- General Theory And Simple Examples

We focus on a Hamiltonian system with a continuous symmetry, and dynamics that takes place on a presymplectic manifold. We explain how the symmetry can become spontaneously broken by a time crystal, that we define as the minimum of the available mechanical free energy that is simultaneously a time dependent solution of Hamilton's equation. The mathematical description of such a timecrystalline spontaneous symmetry breaking builds on concepts of equivariant Morse theory in the space of Hamiltonian flows. As an example we analyze a general family of timecrystalline Hamiltonians that is designed to model polygonal, piecewise linear closed strings. The vertices correspond to the locations of pointlike interaction centers; the string is akin a chain of atoms, that are joined together by covalent bonds, modeled by the links of the string. We argue that the timecrystalline character of the string can be affected by its topology. For this we show that a knotty string is usually more timecrystalline than a string with no self-entanglement. We also reveal a relation between phase space topology and the occurrence of timecrystalline dynamics. For this we show that in the case of three point particles, the presence of a time crystal can relate to a Dirac monopole that resides in the phase space. Our results propose that physical examples of Hamiltonian time crystals can be realized in terms of closed, knotted molecular rings.

nlin.PS↗

arXiv2020

Provenance of classical Hamiltonian time crystals

Classical Hamiltonian systems with conserved charges and those with constraints often describe dynamics on a pre-symplectic manifold. Here we show that a pre-symplectic manifold is also the proper stage to describe autonomous energy conserving Hamiltonian time crystals. We explain how the occurrence of a time crystal relates to the wider concept of spontaneously broken symmetries; in the case of a time crystal, the symmetry breaking takes place in a dynamical context. We then analyze in detail two examples of time crystalline Hamiltonian dynamics. The first example is a piecewise linear closed string, with dynamics determined by a Lie-Poisson bracket and Hamiltonian that relates to membrane stability. We explain how the Lie-Poisson brackets descents to a time crystalline pre-symplectic bracket, and we show that the Hamiltonian dynamics supports two phases; in one phase we have a time crystal and in the other phase time crystals are absent. The second example is a discrete Hamiltonian variant of the Q-ball Lagrangian of time dependent non-topological solitons. We explain how a Q-ball becomes a time crystal, and we construct examples of time crystalline Q-balls.

hep-th↗

arXiv2019

Topologically enhanced time crystals and molecular knots

A time crystal is a time dependent physical system that does not reach a standstill, even in state of minimum energy. Here we show that the stability of a time crystal can be enhanced by its topology. For this we simulate time crystals made of chainlike ensembles of mutually interacting point particles. When we tie the chain into a knot we find that its timecrystalline qualities improve. The theoretical models we consider are widely used in coarse grained descriptions of linear polymers. Thus we expect that physical realizations of time crystals can be found in terms of knotted molecules.

nlin.PS↗

arXiv2019

Can all-atom protein dynamics be reconstructed from the knowledge of C-alpha time evolution?

We inquire to what extent protein peptide plane and side chain dynamics can be reconstructed from knowledge of C-alpha dynamics. Due to lack of experimental data we analyze all atom molecular dynamics trajectories from Anton supercomputer, and for clarity we limit our attention to the peptide plane O atoms and side chain C-beta atoms. We try and reconstruct their dynamics using four different approaches. Three of these are the publicly available reconstruction programs Pulchra, Remo Scwrl4. The fourth, Statistical Method, builds entirely on statistical analysis of Protein Data Bank (PDB) structures. All four methods place the O and C-beta atoms accurately along the Anton trajectories. However, the Statistical Method performs best. The results suggest that under physiological conditions, the all atom dynamics is slaved to that of C-alpha atoms. The results can help improve all atom force fields, and advance reconstruction and refinement methods for reduced protein structures. The results provide impetus for development of effective coarse grained force fields in terms of reduced coordinates.

q-bio.BM↗

arXiv2018

Truncated Dynamics, Ring Molecules and Mechanical Time Crystals

In applications of mechanics, including quantum mechanics, we often consider complex systems, where complete solutions of the underlying "fundamental" equations is both impractical and unnecessary to describe appropriate observations accurately. For example, practical chemistry, including even precision first-principles quantum chemistry, is never concerned with the behavior of the subnuclear quarks and gluons. Instead, we often focus on a few key variables, and construct a so-called effective theory for those. Such effective theories can become complicated and non-local, even for fairly simple systems. But in many circumstances, when there is a separation of scales, we can treat the reduced set of variables as a conventional dynamical system in its own right, governed by an energy conserving Lagrangian or Hamiltonian, in a useful approximation. The structure of that emergent description can display qualitatively new features, notably including reduced dimensionality, manifested through unconventional Poisson brackets. Here we discuss the physical meaning and consequences of such truncated dynamics. We propose physically realizable toy models of molecular rings, wherein time crystals emerge at the classical level. We propose that such behavior occurs in the effective theory of highly diamagnetic aromatic ring molecules, and could be widespread.

physics.class-ph↗

arXiv2017

Virtual reality analysis of intrinsic protein geometry with applications to cis peptide planes

A protein is traditionally visualised as a piecewise linear discrete curve, and its geometry is conventionally characterised by the extrinsically determined Ramachandran angles. However, a protein backbone has also two independent intrinsic geometric structures, due to the peptide planes and the side chains. Here we adapt and develop modern 3D virtual reality techniques to scrutinize the atomic geometry along a protein backbone, in the vicinity of a peptide plane. For this we compare backbone geometry-based (extrinsic) and structure-based (intrinsic) coordinate systems, and as an example we inspect the trans and cis peptide planes. We reveal systematics in the way how a cis peptide plane deforms the neighbouring atomic geometry, and we develop a virtual reality based visual methodology that can identify the presence of a cis peptide plane from the arrangement of atoms in its vicinity. Our approach can easily detect exceptionally placed atoms in crystallographic structures. Thus it can be employed as a powerful visual refinement tool which is applicable also in the case when resolution of the protein structure is limited and whenever refinement is needed. As concrete examples we identify a number of crystallographic protein structures in Protein Data Bank (PDB) that display exceptional atomic positions around their cis peptide planes.

q-bio.BM↗

arXiv2017

Solution X-ray scattering (S/WAXS) and structure formation in protein dynamics

We propose to develop mean field theory in combination with Glauber algorithm, to model and interpret protein dynamics and structure formation in small to wide angle x-ray scattering (S/WAXS) experiments. We develop the methodology by analysing the Engrailed homeodomain protein as an example. We demonstrate how to interpret S/WAXS data with a good precision and over an extended temperature range. We explain experimentally observed phenomena in terms of protein phase structure, and we make predictions for future experiments how the scattering data behaves at different ambient temperature values. We conclude that a combination of mean field theory with Glauber algorithm has the potential to develop into a highly accurate, computationally effective and predictive tool for analysing S/WAXS data. Finally, we compare our results with those obtained previously in an all-atom molecular dynamics simulation.

q-bio.BM↗

arXiv2017

Multiple scales and phases in discrete chains with application to folded proteins

Chiral heteropolymers such as larger globular proteins can simultaneously support multiple length scales. The interplay between different scales brings about conformational diversity, and governs the structure of the energy landscape. Multiple scales produces also complex dynamics, which in the case of proteins sustains live matter. However, thus far no clear understanding exist, how to distinguish the various scales that determine the structure and dynamics of a complex protein. Here we propose a systematic method to identify the scales in chiral heteropolymers such as a protein. For this we introduce a novel order parameter, that not only reveals the scales but also probes the phase structure. In particular, we argue that a chiral heteropolymer can simultaneously display traits of several different phases, contingent on the length scale at which it is scrutinized. Our approach builds on a variant of Kadanoff's block-spin transformation that we employ to coarse grain piecewise linear chains such as the C$α$ backbone of a protein. We derive analytically and then verify numerically a number of properties that the order parameter can display. We demonstrate how, in the case of crystallographic protein structures in Protein Data Bank, the order parameter reveals the presence of different length scales, and we propose that a relation must exist between the scales, phases, and the complexity of folding pathways.

cond-mat.soft↗

arXiv2016

Towards multistage modelling of protein dynamics with monomeric Myc oncoprotein as an example

We propose to combine a mean field approach with all atom molecular dynamics into a multistage algorithm that can model protein folding and dynamics over very long time periods yet with atomic level precision. As an example we investigate an isolated monomeric Myc oncoprotein that has been implicated in carcinomas including those in colon, breast and lungs. Under physiological conditions a monomeric Myc is presumed to be an example of intrinsically disordered proteins, that pose a serious challenge to existing modelling techniques. We argue that a room temperature monomeric Myc is in a dynamical state, it oscillates between different conformations that we identify. For this we adopt the C-alpha backbone of Myc in a crystallographic heteromer as an initial Ansatz for the monomeric structure. We construct a multisoliton of the pertinent Landau free energy, to describe the C-alpha profile with ultra high precision. We use Glauber dynamics to resolve how the multisoliton responds to repeated increases and decreases in ambient temperature. We confirm that the initial structure is unstable in isolation. We reveal a highly degenerate ground state landscape, an attractive set towards which Glauber dynamics converges in the limit of vanishing ambient temperature. We analyse the thermal stability of this Glauber attractor using room temperature molecular dynamics. We identify and scrutinise a particularly stable subset in which the two helical segments of the original multisoliton align in parallel, next to each other. During the MD time evolution of a representative structure from this subset, we observe intermittent quasiparticle oscillations along the C-terminal alpha-helix, some of which resemble a translating Davydov's Amide-I soliton. We propose that the presence of oscillatory motion is in line with the expected intrinsically disordered character of Myc.

q-bio.BM↗

arXiv2016

Thermal unfolding of myoglobin in the Landau-Ginzburg-Wilson approach

The Landau-Ginzburg-Wilson paradigm is applied to model the low-temperature crystallographic C$α$ backbone structure of sperm whale myoglobin. The Glauber protocol is employed to simulate its response to an increase in ambient temperature. The myoglobin is found to unfold from its native state by a succession of $α$-helical intermediates, fully in line with the observed folding and unfolding patterns in denaturation experiments. In particular, a molten globule intermediate is identified with experimentally correct attributes. A detailed, experimentally testable contact map is constructed to characterise the specifics of the unfolding pathway, including the formation of long range interactions. The results reveal how the unfolding process of a protein is driven by the interplay between, and a successive melting of, its modular secondary structure components.

q-bio.BM↗