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A. J. Niemi

Publications and source records attributed to A. J. Niemi.

12 recordsLinked to original sources
arXiv2026

Non-Abelian Geometric Phases in Triangular Structures And Universal SU(2) Control in Shape Space

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 governing adiabatic transport within the $E$-manifold. We show that its restricted holonomy group is $\mathrm{SU}(2)$, 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-$X$ (CNOT) 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($6s$)--Cs($6s$)--Cs($nd_{3/2}$) Rydberg trimer in optical tweezers and specify operating conditions that suppress leakage out of the $E$-manifold.

quant-ph↗
arXiv2015

On phase diagram and the pseudogap state in a linear chiral homopolymer model

The phase structure of a homopolymer chain is investigated in terms of a universal theoretical model, designed to describe the infrared limit of slow spatial variations. The effects of chirality are studied and compared with the influence of a short-range attractive interaction between monomers, at various ambient temperature values. In the high temperature limit the homopolymer chain is in the self-avoiding random walk phase. But at low temperatures, two different phases are possible: When short-range attractive interactions dominate over chirality, the chain collapses into a space- filling conformation. But when the attractive interactions become weaker, there is a low temperature unfolding transition and the chain becomes like a straight rod. Between the high temperature and low temperature limits, several intermediate states are observed. For sufficiently high values of short-range attraction, the conventional θ-regime is observed between the self-avoiding random walk phase and the space filling collapsed phase. But when chirality increases, there is a trasition from the θ-regime to a pseudogap state. Moreover, a regime akin the θ-regime is identified between the pseudogap state, and the low temperature phase where the chain is like a straight rod. Applications to polymers and proteins, in particular collagen, are suggested.

cond-mat.soft↗
arXiv2003

Asymptotically Free Yang-Mills Classical Mechanics with Self-Linked Orbits

We construct a classical mechanics Hamiltonian which exhibits spontaneous symmetry breaking akin the Coleman-Weinberg mechanism, dimensional transmutation, and asymptotically free self-similarity congruent with the beta-function of four dimensional Yang-Mills theory. Its classical equations of motion support stable periodic orbits and in a three dimensional projection these orbits are self-linked into topologically nontrivial, toroidal knots.

hep-th↗
arXiv1997

Toroidal Confugurations As Stable Solitons

Previously we have proposed that in certain relativistic quantum field theories knotlike configurations may appear as stable solitons. Here we present a detailed investigation of the simplest knotted soliton, the torus-shaped unknot.

hep-th↗
arXiv1995

On the Characterization of Classical Dynamical Systems Using Supersymmetric Nonlinear $σ$-models

We construct a two dimensional nonlinear $σ$-model that describes the Hamiltonian flow in the loop space of a classical dynamical system. This model is obtained by equivariantizing the standard N=1 supersymmetric nonlinear $σ$-model by the Hamiltonian flow. We use localization methods to evaluate the corresponding partition function for a general class of integrable systems, and find relations that can be viewed as generalizations of standard relations in classical Morse theory.

hep-th↗
arXiv1994

On the infrared limit of the Chern-Simons-Proca theory

We investigate a modification of the 2+1 dimensional abelian Chern-Simons theory, obtained by adding a Proca mass term to the gauge field. We are particularly interested in the infrared limit, which can be described by two {\it a priori} different "topological" quantum mechanical models. We apply methods of equivariant cohomology and the ensuing supersymmetry to analyze the partition functions of these quantum mechanical models. In particular, we find that a previously discussed phase-space reductive limiting procedure which relates these two models can be seen as a direct consequence of our supersymmetry.

hep-th↗
arXiv1994

Equivariant Morse theory and quantum integrability

We investigate an equivariant generalization of Morse theory for a general class of integrable models. In particular, we derive equivariant versions of the classical Poincaré-Hopf and Gauss-Bonnet-Chern theorems and present the corresponding path integral generalizations. Our approach is based on equivariant cohomology and localization techniques, and is closely related to the formalism developed by Matthai and Quillen in their approach to Gaussian shaped Thom forms.

hep-th↗
arXiv1994

On the Duistermaat-Heckman Integration Formula And Integrable Models

In this article we review the Duistermaat-Heckman integration formula and the ensuing equivariant cohomology structure, in the finite dimensional case. In particular, we discuss the connection between equivariant cohomology and classical integrability. We also explain how the integration formula is derived, and explore some possible new directions that could eventually yield novel integration formulas for nontrivial integrable models.

hep-th↗
arXiv1993

On the Infrared Limit of Two Dimensional QCD

We study the infrared limit of two dimensional QCD, with massless dynamical Dirac fermions that are in the fundamental representation of the gauge group. We find that the theory reduces to a spin generalization of the Calogero model with an additional magnetic coupling which is of the Pauli type.

hep-th↗
arXiv1993

On Quantum Integrability and the Lefschetz Number

Certain phase space path integrals can be evaluated exactly using equivariant cohomology and localization in the canonical loop space. Here we extend this to a general class of models. We consider hamiltonians which are {\it a priori} arbitrary functions of the Cartan subalgebra generators of a Lie group which is defined on the phase space. We evaluate the corresponding path integral and find that it is closely related to the infinitesimal Lefschetz number of a Dirac operator on the phase space. Our results indicate that equivariant characteristic classes could provide a natural geometric framework for understanding quantum integrability.

hep-th↗
arXiv1992

Index Theorems and Loop Space Geometry

We investigate the evaluation of the Dirac index using symplectic geometry in the loop space of the corresponding supersymmetric quantum mechanical model. In particular, we find that if we impose a simple first class constraint, we can evaluate the Callias index of an odd dimensional Dirac operator directly from the quantum mechanical model which yields the Atiyah-Singer index of an even dimensional Dirac operator in one more dimension. The effective action obtained by BRST quantization of this constrained system can be interpreted in terms of loop space symplectic geometry, and the corresponding path integral for the index can be evaluated exactly using the recently developed localization techniques.

hep-th↗