MIT Center for Theoretical Physics — a Leinweber Institute Publications

Quantum thermalization describes how closed quantum systems can effectively reach thermal equilibrium, resolving the apparent incongruity between the reversibility of Schrödinger's equation and the irreversible entropy growth dictated by the second law of thermodynamics. Despite its ubiquity and conceptual significance, a complete proof of quantum thermalization has remained elusive for several decades. Here, we prove that quantum thermalization must occur in any qubit system with local interactions satisfying three conditions: (i) high effective temperature, (ii) translation invariance, and (iii) no perfect resonances in the energy spectrum. Specifically, we show that a typical, initially unentangled pure state drawn from any ensemble with maximum entropy becomes locally indistinguishable from a Gibbs state upon unitary evolution. Our proof relies on a recent breakthrough in quantum information theory proving the separability of high-temperature thermal states, as well as on new technical results identifying sufficient conditions for quantum thermalization, whose applicability extends beyond our main result. Our work illustrates that statistical physics can be understood as an emergent phenomenon, explicitly derived from the first principles of quantum mechanics.

Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized compiling, a technique that promotes a unitary gate to a quantum channel and enables a quadratic suppression of error (i.e., ϵ → O(ϵ${}^{}$)) at little to no overhead. Here we integrate randomized compiling into QSP through Stochastic Quantum Signal Processing. Our algorithm implements a probabilistic mixture of polynomials, strategically chosen so that the average evolution converges to that of a target function, with an error quadratically smaller than that of an equivalent individual polynomial. Because nearly all QSP-based algorithms exhibit query complexities scaling as $O(\log (1/ϵ))$—stemming from a result in functional analysis—this error suppression reduces their query complexity by a factor that asymptotically approaches 1/2. By the unifying capabilities of QSP, this reduction extends broadly to quantum algorithms, which we demonstrate on algorithms for real and imaginary time evolution, phase estimation, ground state preparation, and matrix inversion.

We derive an analog of Mirzakhani’s recursion relation for hyperbolic string vertices and investigate its implications for closed string field theory. Central to our construction are systolic volumes: the Weil-Petersson volumes of regions in moduli spaces of Riemann surfaces whose elements have systoles L ≥ 0. These volumes can be shown to satisfy a recursion relation through a modification of Mirzakhani’s recursion as long as L ≤ 2 sinh${}^{}$ 1. Applying the pants decomposition of Riemann surfaces to off-shell string amplitudes, we promote this recursion to hyperbolic string field theory and demonstrate the higher order vertices are determined by the cubic vertex iteratively for any background. Such structure implies the solutions of closed string field theory obey a quadratic integral equation. We illustrate the utility of our approach in an example of a stubbed scalar theory.

We point out that dark matter can illuminate planetary skies via ultraviolet airglow. Dark matter annihilation products can excite molecular hydrogen, which then deexcites to produce ultraviolet emission in the Lyman and Werner bands. We search for this new effect by analyzing nightside ultraviolet radiation data from Voyager 1, Voyager 2, and New Horizons flybys of Neptune, Uranus, Saturn, and Jupiter. Our findings set new constraints on the dark matter-nucleon scattering cross section down to about ${10}^{-40}$cm${}^2$. We highlight that future ultraviolet airglow measurements of Solar System planets or other worlds provide a new dark matter discovery avenue.

The temperature and polarization anisotropies of the cosmic microwave background have been used to set constraints on decaying dark matter models down to keV masses. In this work, we extend these limits down to the sub-keV mass range. Using principal component analysis, we estimate the lower bound on the decay lifetime for a basis of different dark matter masses and Standard Model final states, from which the bound on an arbitrary model can be calculated. We validate our principal component analysis using Markov chain Monte Carlo methods and Planck 2018 data. We perform a separate analysis for models decaying into photons below the hydrogen ionization threshold. We demonstrate that, for these models, the effect of energy deposition can be captured approximately by a single parameter, but the redshift dependence of the effect is very different from higher-energy injections; in particular, the perturbations to cosmic microwave background anisotropies are more sensitive to energy deposited around the time of recombination.

A system with a one-form global symmetry at finite temperature can be viewed as a dissipative fluid of string-like objects. In this work, we classify and construct the most general effective field theories for hydrodynamics of such string fluids, in a probe limit where the one-form charge density is decoupled from the energy-momentum tensor. We show that at leading order in the derivative expansion, there are two distinct types of diffusive transport in a string fluid depending on the discrete spacetime symmetries present in it. One particular application of interest is magnetohydrodynamics (MHD), where the effective field theories describe the diffusion of magnetic field lines. Due to the distinction between the effective field theories for different discrete symmetries, we show that the MHD of a fluid with charge conjugation symmetry is qualitatively different from that of a neutron star, which we previously discussed in arXiv:2207.01636. The explicit effective actions that we write down can be used to obtain the dispersion relations ω(κ) up to cubic order in momenta for each of the different discrete symmetry choices. As another application of this formalism, we show that when the one-form symmetry is spontaneously broken, the effective action reduces to the Maxwell theory. This confirms the interpretation of the photon as a Goldstone boson arising from the spontaneous breaking of a one-form symmetry.

We take a first step towards developing a new language to describe causal structure, event horizons, and quantum extremal surfaces (QES) for the bulk description of holographic systems beyond the standard Einstein gravity regime. By considering the structure of boundary operator algebras, we introduce a stringy causal depth parameter'', which quantifies the depth of the emergent radial direction in the bulk, and a certain notion of ergodicity on the boundary. We define stringy event horizons in terms of the half-sided inclusion property, which is related to a stronger notion of boundary ergodic or quantum chaotic behavior. Using our definition, we argue that above the Hawking--Page temperature, there is an emergent sharp horizon structure in the large N limit of N=4 Super-Yang--Mills at finite nonzero 't Hooft coupling. In contrast, some previously considered toy models of black hole information loss do not have a stringy horizon. Our methods can also be used to probe violations of the equivalence principle for the bulk gravitational system, and to explore aspects of stringy nonlocality.

The so-called metastability bound asserts that an unnaturally small Higgs mass is a necessary condition for electroweak vacuum metastability, offering a new approach toward solving the hierarchy problem. So far, this result relies on the assumption of a negative Higgs mass parameter, or equivalently, on electroweak spontaneous symmetry breaking. We derive a new, corresponding bound for the case of a positive mass parameter. When the new bound is significantly more restrictive than or comparable to its established counterpart, it may offer an explanation for the sign of the Higgs mass parameter, and thus, spontaneous symmetry breaking itself. New physics at scales δ(1–10) TeV can lower these bounds as far as the TeV scale. As an illustration, we consider vacuum stability in the presence of additional TeV-scale fermions with Yukawa couplings to the Higgs, as well as a dimension-six term parametrizing new physics in the UV. This scenario requires new physics that couples strongly to the Higgs, and can potentially be probed at future colliders. Finally, to allow for comparison with concrete mechanisms predicting metastability, we provide the mass-dependent lifetime of the electroweak vacuum for this model.

The abundance of massive primordial black holes has historically been constrained by dynamical probes. Since these objects can participate in hard few-body scattering processes, they can readily transfer energy to stellar systems and, in particular, disrupt wide binaries. However, disruption is not the only possible outcome of such few-body processes. Primordial black holes could also participate in exchange processes, in which one component of a binary system is ejected and replaced by the black hole itself. In this case, the remaining object in the binary would dynamically appear to have an invisible companion. We study the rate of exchange processes for primordial black holes as a component of dark matter and evaluate possible mechanisms for detecting such binaries. We find that many such binaries plausibly exist in the Solar neighborhood and show that this process can account for observed binary systems whose properties run counter to the predictions of isolated binary evolution.

The abundance of massive primordial black holes has historically been constrained by dynamical probes. Since these objects can participate in hard few-body scattering processes, they can readily transfer energy to stellar systems and, in particular, disrupt wide binaries. However, disruption is not the only possible outcome of such few-body processes. Primordial black holes could also participate in exchange processes, in which one component of a binary system is ejected and replaced by the black hole itself. In this case, the remaining object in the binary would dynamically appear to have an invisible companion. We study the rate of exchange processes for primordial black holes as a component of dark matter and evaluate possible mechanisms for detecting such binaries. We find that many such binaries plausibly exist in the Solar neighborhood and show that this process can account for observed binary systems whose properties run counter to the predictions of isolated binary evolution.

The black hole entropy has been observed to generically turn negative at exponentially low temperatures \(T\sim e^{-S_0}\) in the extremal Bekenstein-Hawking entropy \(S_0\), a seeming pathology often attributed to missing non-perturbative effects. In fact, we show that this negativity must happen for any effective theory of quantum gravity with an ensemble description. To do so, we identify the usual gravitational entropy as an annealed entropy \(S_a\), and prove that this quantity gives \(S_0\) at extremality if and only if the ground-state energy is protected by supersymmetry, and diverges negatively otherwise. The actual thermodynamically-behaved quantity is the average or quenched entropy \(S_q\), whose calculation is poorly understood in gravity: it involves replica wormholes in a regime where the topological expansion breaks down. Using matrix integrals we find new instanton saddles that dominate gravitational correlators at \(T\sim e^{-S_0}\) and are dual to semiclassical wormholes involving dynamical branes. These brane solutions give the leading contribution to any black hole very near extremality, and a duality with matrix ensembles would not make sense without them. In the non-BPS case, they are required to make \(S_q\) non-negative and also enhance the negativity of \(S_a\), both effects consistent with matrix integrals evaluated exactly. Our instanton results are tested against the on-shell action of D3-branes dual to multiply wrapped Wilson loops in \(\mathcal{N}=4\) super-YM, and a precise match is found. Our analysis of low-energy random matrix spectra also explains the origin of spectral gaps in supersymmetric theories, not only when there are BPS states at zero energy, but also for purely non-BPS supermultiplets. In the former, our prediction for the gap in terms of the degeneracy of BPS states agrees with the R-charge scaling in gapped multiplets of \(\mathcal{N}=2\) super-JT gravity.

As the partons in a jet propagate through the quark-gluon plasma (QGP) produced in a heavy-ion collision, they lose energy to, kick, and are kicked by the medium. The resulting modifications to the parton shower encode information about the microscopic nature of QGP. The momentum and energy lost by the parton shower are gained by the medium and, since QGP is a strongly coupled liquid, this means that the jet excites a wake in the droplet of QGP. After freezeout, this wake becomes soft hadrons with net momentum in the jet direction meaning that reconstructed jets include hadrons originating from both the modified parton shower and its wake. This makes it challenging to find an unambiguous experimental view of the response of a droplet of QGP to a jet. Recent years have seen significant advances in the understanding of the substructure of jets using correlation functions of the energy flux operator. So far, such studies have focused primarily on the two-point correlator, which serves to identify the angular scale of the underlying dynamics. Higher-point correlators hold the promise of mapping out the dynamics themselves. We perform the first study of the shape-dependent three-point energy-energy-energy correlator in heavy-ion collisions. Using the Hybrid Model to simulate the interactions of high energy jets with QGP, we show that hadrons originating from wakes are the dominant contribution to the three-point correlator in the regime where the three points are well-separated in angle, forming a roughly equilateral triangle. This equilateral region of the correlator is far from the region populated by collinear vacuum emissions, making it a canvas on which jet wakes can be imaged. Our work is a key step towards the systematic use of energy correlators to image and unravel the dynamical response of a droplet of QGP to a passing jet, and motivates many experimental and theoretical studies.

Deconvolving ("unfolding'') detector distortions is a critical step in the comparison of cross section measurements with theoretical predictions in particle and nuclear physics. However, most existing approaches require histogram binning while many theoretical predictions are at the level of statistical moments. We develop a new approach to directly unfold distribution moments as a function of another observable without having to first discretize the data. Our Moment Unfolding technique uses machine learning and is inspired by Generative Adversarial Networks (GANs). We demonstrate the performance of this approach using jet substructure measurements in collider physics. With this illustrative example, we find that our Moment Unfolding protocol is more precise than bin-based approaches and is as or more precise than completely unbinned methods.

Quantum dynamics can be analyzed via the structure of energy eigenstates. However, in the many-body setting, preparing eigenstates associated with finite temperatures requires time scaling exponentially with system size. In this work we present an efficient quantum search algorithm which produces quasi-stationary states, having energies supported within narrow windows of a dense many-body spectrum. In time scaling polynomially with system size, the algorithm produces states with inverse polynomial energy width, which can in turn be used to analyze many-body dynamics out to polynomial times. The algorithm is based on quantum singular value transformations and quantum signal processing, and provides a quadratic speedup over measurement-based approaches. We discuss how this algorithm can be used as a primitive to investigate the mechanisms underlying thermalization and hydrodynamics in many-body quantum systems.

We present an exact solution for the linearized junction array modes of the superconducting qubit fluxonium in the absence of array disorder. This solution holds for arrays of any length and ground capacitance, and for both differential and grounded devices. Array mode energies are determined by roots of convex combinations of Chebyshev polynomials, and their spatial profiles are plane waves. We also provide a simple, approximate solution, which estimates array mode properties over a wide range of circuit parameters, and an accompanying Mathematica file that implements both the exact and approximate solutions.

Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way and are generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian modulated symmetries in \({1+1}\) dimensions. Working with local Hamiltonians of spin chains, we explore the dual symmetries after gauging and their potential new spatial modulations. We establish sufficient conditions for the existence of an isomorphism between the modulated symmetries and their dual, naturally implemented by lattice reflections. For instance, in systems of prime qudits, translation invariance guarantees this isomorphism. For non-prime qudits, we show using techniques from ring theory that this isomorphism can also exist, although it is not guaranteed by lattice translation symmetry alone. From this isomorphism, we identify new Kramers-Wannier dualities and construct related non-invertible reflection symmetry operators using sequential quantum circuits. Notably, this non-invertible reflection symmetry exists even when the system lacks ordinary reflection symmetry. Throughout the paper, we illustrate these results using various simple toy models.

Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the non-perturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials. Agreement is seen with chiral perturbation theory predictions when the chemical potential is small. Comparison to perturbative QCD calculations at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential, \(\mu_I\), bounds the partition function for a baryon chemical potential \(\mu_B=3/2\mu_I\), these calculations also provide rigorous non-perturbative QCD bounds on the nuclear equation of state over a wide range of baryon densities for the first time.

Gravitational lensing data is frequently collected at low resolution due to instrumental limitations and observing conditions. Machine learning-based super-resolution techniques offer a method to enhance the resolution of these images, enabling more precise measurements of lensing effects and a better understanding of the matter distribution in the lensing system. This enhancement can significantly improve our knowledge of the distribution of mass within the lensing galaxy and its environment, as well as the properties of the background source being lensed. Traditional super-resolution techniques typically learn a mapping function from lower-resolution to higher-resolution samples. However, these methods are often constrained by their dependence on optimizing a fixed distance function, which can result in the loss of intricate details crucial for astrophysical analysis. In this work, we introduce \(\texttt{DiffLense}\), a novel super-resolution pipeline based on a conditional diffusion model specifically designed to enhance the resolution of gravitational lensing images obtained from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). Our approach adopts a generative model, leveraging the detailed structural information present in Hubble Space Telescope (HST) counterparts. The diffusion model, trained to generate HST data, is conditioned on HSC data pre-processed with denoising techniques and thresholding to significantly reduce noise and background interference. This process leads to a more distinct and less overlapping conditional distribution during the model's training phase. We demonstrate that \(\texttt{DiffLense}\) outperforms existing state-of-the-art single-image super-resolution techniques, particularly in retaining the fine details necessary for astrophysical analyses.