arXiv subjects

Thomas D. Cohen

Publications and source records attributed to Thomas D. Cohen.

At least 19 recordsLinked to original sources

arXiv2026

The massive Thirring / sine-Gordon model with non-zero current density

This paper determines the zero-temperature equation of state for the massive Thirring / sine-Gordon model. This demonstrates recently derived model-independent upper and lower bounds on the zero-temperature equation of state with fixed number density from systems with a non-zero current density. That approach is potentially valuable as Monte Carlo calculations with a current density avoid the sign problem in the Euclidean formulation. An advantage to illustrating these bounds in the massive Thirring / sine-Gordon model is that the relevant calculations with both a number density and a current density can be done using a Bethe ansatz. For this model, optimal bounds constrain the energy density as a function of number density by a factor of two from above and below at high densities for all choices of couplings. The lower bound becomes exact at low densities, while the upper bound approaches the worst constraint of a factor of 4.90.

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arXiv2026

A method to obtain bounds on the equation of state of cold nuclear matter from imaginary chemical potentials

The sign problem in numerical calculations of the QCD Euclidean space path integral of QCD with a chemical potential vanishes if the chemical potential is imaginary. Moreover, calculations of the partition function with imaginary chemical potentials are equivalent to calculations with Lagrange multipliers enforcing the current density. At zero temperature, Lorentz boosts allow one to deduce properties of systems with both number density and current density from properties of systems with a current density alone; this allows both upper and lower bounds to be determined for the equation of state (EOS) in the form of energy density as a function of number density.

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arXiv2026

The Silver Blaze Problem in QCD

This article provides a pedagogical introduction to the Silver Blaze problem. This problem refers to the difficulty of reconciling to perspectives on QCD with a chemical potential. The first is the phenomenological fact that at $T=0$ QCD remains in its ground state -- the vacuum -- with all physical observables unchanged whenever the magnitude of a chemical potential is less than some critical value. The second is the fact that in functional integral treatments, the inclusion of any nonzero chemical potential changes all eigenvalues of the Dirac operator for every gauge configuration, leading to a natural expectation that the functional determinants also changes, which leads to the expectation that physical observables should be altered. The problem amounts to explaining why nothing happens below the critical chemical potential. By focusing on the eigenvalues of $γ_0$ times the Dirac operator rather than the Dirac operator itself, it is possible to show that for QCD with two flavors and identical quark masses, an isospin chemical potential with a magnitude less than $m_π$ (and no baryon chemical potential), or a baryon chemical potential of less than $\frac{3}{2} m_π$ (and no isospin chemical potential), the functional integerals at $T=0$ themselves remain unchanged in all configurations that contribute to the functional integral with non-vanishing weight. However, for $μ_{\rm crit}μ_B > \frac{3}{2} m_π$, the Silver Blaze phenomenon arises due to functional determinants having nontrivial phases that lead to cancellations between different gauge configurations. The mechanism leading to such cancellations remains unknown.

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arXiv2026

Numerical study of computational cost of maintaining adiabaticity for long paths

Recent work argued that the scaling of a dimensionless quantity $Q_D$ with path length is a better proxy for quantifying the scaling of the computational cost of maintaining adiabaticity than the timescale. It also conjectured that generically the scaling will be superlinear (although special cases exist in which it is linear). The quantity $Q_D$ depends only on the properties of ground states along the Hamiltonian path and the rate at which the path is followed. In this paper, we demonstrate that this conjecture holds for simple Hamiltonian systems that can be studied numerically. In particular, the systems studied exhibit the behavior that $Q_D$ grows approximately as $L \log L$ where $L$ is the path length when the threshold error is fixed.

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arXiv2025

Practical limitations of the switching theorem for adiabatic state preparation

The viability of adiabatic quantum computation depends on the slow evolution of the Hamiltonian. The adiabatic switching theorem provides an asymptotic series for error estimates in $1/T$, based on the lowest non-zero derivative of the Hamiltonian and its eigenvalues at the endpoints. Modifications at the endpoints in practical implementations can modify this scaling behavior, suggesting opportunities for error reduction by altering endpoint behavior while keeping intermediate evolution largely unchanged. Such modifications can significantly reduce errors for long evolution times, but they may also require exceedingly long timescales to reach the hyperadiabatic regime, limiting their practicality. This paper explores the transition between the adiabatic and hyperadiabatic regimes in simple low-dimensional Hamiltonians, highlighting the impact of modifications of the endpoints on approaching the asymptotic behavior described by the switching theorem.

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arXiv2025

Gauge invariance and color charge fluctuations

The nature of confinement is connected with color charge. Unfortunately, the color charge densities in QCD, the Noether charge densities associated with the global color invariance, are not invariant under local color rotations. This implies that the expectation values of the net color charge in any region of any physical state in QCD, states that satisfy the color Gauss law, are automatically zero for all components of color. In this paper it is shown that the expectation value of the square of the net color charge in a region, a measure of the color charge fluctuations, is necessarily nonzero when evaluated in physical states and the result, while depending on the scheme and scale by which the theory is regulated, is gauge invariant. This holds despite the formal lack of gauge invariance of the operator. Moreover, there is a particular combination of the color charge fluctuations for the vacuum and for a system describable by a non-trivial density matrix that is independent that has a well-defined continuum limit

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arXiv2025

Asymptotic errors in adiabatic evolution

The adiabatic theorem in quantum mechanics implies that if a system is in a discrete eigenstate of a Hamiltonian and the Hamiltonian evolves in time arbitrarily slowly, the system will remain in the corresponding eigenstate of the evolved Hamiltonian. Understanding corrections to the adiabatic result that arise when the evolution of the Hamiltonian is slow -- but not arbitrarily slow -- has become increasingly important, especially since adiabatic evolution has been proposed as a method of state preparation in quantum computing. This paper identifies two regimes, an adiabatic regime in which corrections are generically small and can depend on details of the evolution throughout the path, and a hyperadiabatic regime in which the error is given by a form similar to an asymptotic expansion in the inverse of the evolution time with the coefficients depending principally on the behavior at the endpoints. However, the error in this hyperadiabatic regime is neither given by a true asymptotic series nor solely dependent on the endpoints: the coefficients combine the contributions from both endpoints, with relative phase factors that depend on the average spectral gaps along the trajectory, multiplied by the evolution time. The central result of this paper is to identify a quantity, referred to as the typical error, which is obtained by appropriately averaging the error over evolution times that are small compared to the evolution time itself. This typical error is characterized by an asymptotic series and depends solely on the endpoints of the evolution, remaining independent of the details of the intermediate evolution.

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arXiv2024

Corrections to adiabatic behavior for long paths

The cost and the error of the adiabatic theorem for preparing the final eigenstate are discussed in terms of path length. Previous studies in terms of the norm of the Hamiltonian and its derivatives with the spectral gap are limited in their ability to describe the cost of adiabatic state preparation for certain physically large systems. We argue that total time is not a good measure for determining the computational difficulty of adiabatic quantum computation by developing a no-go theorem. From the result of time-periodic Hamiltonian cases, we suggest that there are proxies for computational cost which typically grow as path length increases when the error is kept fixed and small and consider possible conjectures on how general the behavior is.

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arXiv2024

Zeno Effect Suppression of Gauge Drift in Quantum Simulations

Quantum simulation of lattice gauge theories is a promising tool for the study of many complicated problems including ones with real-time dynamics. For gauge theories, however, there is a major challenge in maintaining gauge invariance during time evolution. Such theories have a full Hilbert space that is larger than the physical space -- the set of states which are gauge invariant or equivalently respect the Gauss law. While an exact implementation of Hamiltonian dynamics starting in the physical Hilbert space will keep the system in the physical space, various types of errors will inevitably produce components outside of it. This work proposes a method of suppressing this gauge drift via the Zeno effect. As in the standard picture of the Zeno effect, our method relies on frequent projection onto the physical subspace. Additionally, a technique is discussed to reduce the speed of the gauge drift, which helps to reduce the required frequency of projections. We demonstrate our method on a $\mathbb{Z}_2$ gauge theory toy model.

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arXiv2024

Efficient vacuum state preparation for quantum simulation of strongly interacting local quantum field theories

We present an efficient approach for preparing ground states in the context of strongly interacting local quantum field theories on quantum computers. The approach produces the vacuum state in a time proportional to the square-root of the volume, which is a square-root improvement in speed compared to traditional approaches. The approach exploits a novel method for traversing the path in parameter space in which the resources scale linearly with a path length suitably defined in parameter space. Errors due to practical limitations are controlled and do not exhibit secular growth along the path. The final accuracy can be arbitrarily improved with an additive cost, which is independent of the volume and grows slower than logarithmically with the overlap between the state produced and the exact ground state. We expect that the method could potentially hold practical value not only within the realm of quantum field theories but also in addressing other challenges involving long path lengths.

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arXiv2023

Optimizing rodeo projection

The rodeo algorithm has been proposed recently as an efficient method in quantum computing for projection of a given initial state onto a state of fixed energy for systems with discrete spectra. In the initial formulation of the rodeo algorithm these times were chosen randomly via a Gaussian distribution with fixed RMS times. In this paper it is shown that such a random approach for choosing times suffers from exponentially large fluctuations in the suppression of unwanted components: as the number of iterations gets large, the distribution of suppression factors obtained from random selection approaches a log-normal distribution leading to remarkably large fluctuations. We note that by choosing times intentionally rather than randomly such fluctuations can be avoided and strict upper bounds on the suppression can be obtained. Moreover, the average suppression using fixed computational cost can be reduced by many orders of magnitude relative to the random algorithm. A key to doing this is to choose times that vary over exponentially many times scales, starting from a modest maximum scale and going down to time scales exponentially smaller.

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arXiv2023

Boltzmann Distributions on a Quantum Computer via Active Cooling

Quantum computing raises the possibility of solving a variety of problems in physics that are presently intractable. A number of such problems involves the physics of systems in or near thermal equilibrium. There are two main ways to compute thermal expectation values on a quantum computer: construct a thermal state that reproduces thermal expectation values, or sample various energy eigenstates from a Boltzmann distribution of a given temperature. In this paper we address the second approach and propose an algorithm that uses active cooling to produce the distribution. While this algorithm is quite general and applicable to a wide variety of systems, it was developed with the specific intention of simulating thermal configurations of non-Abelian gauge theories such as QCD, which would allow the study of quark-gluon plasma created in heavy-ion collisions.

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arXiv2022

Pure gauge theories and spatial periodicity

Properties of pure gauge theories in thermal equilibrium as calculated via standard functional integral treatments are mathematically identical to ground state properties of a theory with spatially-periodic boundary conditions imposed on the gauge fields. Such a theory has states that have no analog in a theory in which only physical observables associated with gauge-invariant operators are required to be periodic, rather than the gauge fields themselves; these states are in topological sectors that do not exist in the unconstrained theory. The topology arises because the boundary conditions in the functional integral are gauge invariant on a cylinder but not in the unconstrained theory.

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arXiv2021

A Somewhat Random Walk Through Nuclear and Particle Physics

These notes are an outgrowth of an advanced undergraduate course taught at the University of Maryland, College Park. They are intended as an introduction to various aspects of particle and nuclear physics with an emphasis on the role of symmetry. The basic philosophy is to introduce many of the fundamental ideas in nuclear and particle physics using relatively sophisticated mathematical tools -- but to do so in as a simplified a context to explain the underlying ideas. Thus, for example, the Higgs mechanism is discussed in terms of an Abelian Higgs model. The emphasis is largely, but not entirely theoretical in orientation. The goal is for readers to develop an understanding of many of the underlying issues in a relatively sophisticated way.

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arXiv2021

Quantum algorithms for transport coefficients in gauge theories

In the future, ab initio quantum simulations of heavy ion collisions may become possible with large-scale fault-tolerant quantum computers. We propose a quantum algorithm for studying these collisions by looking at a class of observables requiring dramatically smaller volumes: transport coefficients. These form nonperturbative inputs into theoretical models of heavy ions; thus, their calculation reduces theoretical uncertainties without the need for a full-scale simulation of the collision. We derive the necessary lattice operators in the Hamiltonian formulation and describe how to obtain them on quantum computers. Additionally, we discuss ways to efficiently prepare the relevant thermal state of a gauge theory.

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arXiv2021

The thermodynamics of large-N QCD and the nature of metastable phases

In the limit of a large number of colors (N), both Yang-Mills and quantum chromodynamics are expected to have a first-order phase transition separating a confined hadronic phase and a deconfined plasma phase. One aspect of this separation is that at large N, one can unambiguously identify a plasma regime that is strongly coupled. The existence of a first-order transition suggests that the hadronic phase can be superheated and the plasma phase supercooled. The supercooled deconfined plasma present at large N, if it exists, has the remarkable property that it has negative absolute pressure -- i.e. a pressure below that of the vacuum. For energy densities of order unity in a 1/N expansion but beyond the endpoint of the hadronic superheated phase, a description of homogeneous matter composed of ordinary hadrons with masses of order unity in a 1/N expansion can exist, and acts as though it has a temperature of $T_H$ in order unity. However, the connection between the canonical and microcanonical descriptions breaks down and the system cannot fully equilibrate as $N \rightarrow \infty$. Rather, in a hadronic description, energy is pushed to hadrons with masses that are arbitrarily large. The thermodynamic limit of large volumes becomes subtle for such systems: the energy density is no longer intensive. These conclusions follow provided that standard large N scaling rules hold, the system at large N undergoes a generic first-order phase transition between the hadronic and plasma phases and that the mesons and glueballs follow a Hagedorn-type spectrum.

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arXiv2019

Precision Model-Independent Bounds from Global Analysis of $b \to c \ell ν$ Form Factors

We present a model-independent global analysis of hadronic form factors for the semileptonic decays $b\rightarrow c\ellν$ that exploits lattice-QCD data, dispersion relations, and heavy-quark symmetries. The analysis yields predictions for the relevant form factors, within quantifiable bounds. These form factors are used to compute the semileptonic ratios $R(H_c)$ and various decay-product polarizations. In particular, we find $R(D_s^*)=0.20(3)$ and $R(J/ψ)=0.25(3)$, predictions that can be compared to results of upcoming LHCb measurements. In developing this treatment, we obtain leading-order NRQCD results for the nonzero-recoil relations between the $B_c^+ \rightarrow \{J/ψ, η_c \}$ form factors.

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arXiv2019

Yields of weakly-bound light nuclei as a probe of the statistical hadronization model

The statistical hadronization model is a simple and efficient phenomenological framework in which the relative yields for very high energy heavy ion collisions are essentially determined by a single model parameter---the chemical freeze-out temperature. Recent measurements of yields of hadrons and light nuclei covering over 9 orders of magnitudes from the ALICE collaboration at the LHC were described by the model with remarkable accuracy with a chemical freeze-out temperature of 156.5 $\pm$ 1.5 MeV. A key physical question is whether the freeze-out temperature can be understood, literally, as the temperature at which the various species of an equilibrated gas of hadrons (including resonances) and nuclei chemically freeze out as the model assumes, or whether it successfully parametrizes the yield data for a different reason. The yields of weakly-bound light nuclei---the deuteron and the hypertriton---provide insights into this issue. The analysis indicates that a key assumption underlying the model---that hadrons (and nuclei), just prior to chemical freeze-out temperature, are in thermal equilibrium and are sufficiently dilute as to have particle distributions accurately described statistically by a nearly ideal gas of hadrons and nuclei with masses given by their free space values---appears to be inconsistent with the chemical freeze-out temperature output by the model, at least for these weakly-bound nuclei.

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