Antti J. Niemi

We construct holonomic quantum gates for qubits that are encoded in the near-degenerate vibrational E doublet of a deformable three-body system. Using Kendall's shape theory, we derive the Wilczek-Zee connection that governs adiabatic transport within the E manifold. We show that its restricted holonomy group is SU ( 2 ) , implying universal single-qubit control by closed loops in shape space. We provide explicit loops implementing a π / 2 phase gate and a Hadamard-type gate. For two-qubit operations, we outline how linked holonomic cycles in arrays generate a controlled Chern-Simons phase, enabling an entangling controlled- X () gate. We present a Ramsey-echo interferometric protocol that measures the Wilson loop trace of the Wilczek-Zee connection for a control cycle, providing a gauge-invariant signature of the non-Abelian holonomy. As a physically realizable demonstrator, we propose bond-length modulations of a Cs( 6 s )-Cs( 6 s )-Cs( n d 3 / 2 ) Rydberg trimer in optical tweezers and specify operating conditions that suppress leakage out of the E manifold.

We present a geometric framework for Hamiltonian quantum time crystals, emphasizing the pivotal role of continuous symmetries and their associated conserved charges. In this approach, a time crystal is identified as a minimum-energy ground state that is parallel transported along a family of Fock spaces, with time evolution realized as a symmetry transformation. This parallel transport is implemented via a generalized, time-dependent Bogoliubov transformation, ensuring coherence across the Fock spaces. Revisiting Goldstone’s original analysis, we show that in the presence of a time crystal, the Goldstone mode acquires a mass and its direction oscillates periodically in Higgs space. Our formulation circumvents existing no-go theorems that would otherwise forbid quantum time-crystalline order. We place time crystals within the broader context of quantum many-body physics and field theory, drawing analogies to superconductivity and quantum field theory in time-dependent backgrounds.

Methods of local topology are introduced to the field of protein physics. This is done by interpreting the folding and unfolding processes of a globular protein in terms of conformational bifurcations that alter the local topology of the proteins C α backbone. The mathematical formulation extends Arnold's perestroikas 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 Schrödinger 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. Published by the American Physical Society 2025

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.

Cats have an instinctive ability to use the connection governing parallel transport in the space of shapes to land safely on their feet. Here, we argue that the concept of connection, which is extensively used in general relativity and other parts of theoretical physics, also explains the impressive performance of molecular motors by enabling molecules to evade the conclusions of Feynman’s ratchet-and-pawl analysis. First, we demonstrate the emergence of directed rotational motion from shape changes, which is independent of angular momentum. Then, we computationally design knotted polyalanine molecules and demonstrate the organization of individual atom thermal vibrations into collective rotational motion, which is independent of angular momentum. The motion occurs effortlessly even in ambient water and can be further enhanced through spontaneous symmetry breaking, rendering the molecule an effective theory time crystal. Our findings can be experimentally verified via nuclear magnetic resonance measurements and hold practical potential for molecular motor design and engineering.

In this paper, a novel discrete algebra is presented which follows by combining the SU(2) Lie-Poisson bracket with the discrete Frenet equation. Physically, the construction describes a discrete piecewise linear string in R3. The starting point of our derivation is the discrete Frenet frame assigned at each vertix of the string. Then the link vector that connect the neighbouring vertices assigns the SU(2) Lie-Poisson bracket. Moreover, the same bracket defines the transfer matrices of the discrete Frenet equation which relates two neighbouring frames along the string. The procedure extends in a self-similar manner to an infinite hierarchy of Poisson structures. As an example, the first descendant of the SU(2) Lie-Poisson structure is presented in detail. For this, the spinor representation of the discrete Frenet equation is employed, as it converts the brackets into a computationally more manageable form. The final result is a nonlinear, nontrivial and novel Poisson structure that engages four neighbouring vertices.

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 Poincar\'e 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.