arXiv subjects

C. W. J. Beenakker

Publications and source records attributed to C. W. J. Beenakker.

At least 19 recordsLinked to original sources

arXiv2026

Phonon Scharnhorst effect: Acoustic analogue of the vacuum-fluctuation-boosted speed of light

The Scharnhorst effect in quantum electrodynamics predicts a superluminal velocity shift $δc>0$ at low photon frequencies due to vacuum fluctuations between two mirrors. Although theoretically robust (no causality violation), the effect is extraordinarily small ($δc/c\approx 10^{-32}$ for mirrors $1\,μ{\rm m}$ apart) and outside current experimental reach. Here we propose a condensed matter analogue, replacing the photons in the electromagnetic vacuum by phonon excitations of a Bose-Einstein condensate. In an idealized geometry, the two-dimensional surface of a cylinder (circumference $L$) at zero temperature, the axial speed of sound is increased due to zero-point fluctuations of the condensate by $δc/c\simeq 5\times 10^{-3}\,\tilde{g}$ at $L\simeq 2\,ξ$, to first order in the dimensionless interaction constant $\tilde{g}\simeq 10^{-1}$ of the Bose gas of healing length $ξ\simeq 1\,μ{\rm m}$. This is 28 orders of magnitude larger than the photonic effect, basically because phonons have a self-interaction while photons only interact via massive electrons. We discuss the prospects for observation of the acoustic Scharnhorst effect, the main restriction being the low-temperature requirement.

cond-mat.quant-gas↗

arXiv2026

Symmetric mass generation of interacting chiral fermions on a one-dimensional lattice without fermion doubling

Symmetric mass generation is the interaction-induced opening of a fermion gap without spontaneous symmetry breaking. The anomaly-free 3-4-5-0 model of Wang and Wen provides a minimal one-dimensional setting for this phenomenon, but a direct lattice realization faces two obstacles: fermion doubling for local chiral discretizations and perturbative irrelevance of the six-fermion gapping interaction. We address both obstacles. First, we formulate the model on a strictly one-dimensional tangent-fermion lattice, where a nonlocal hopping produces a single chiral branch without a mirror partner while retaining an efficient tensor-network representation. Second, we add a Hubbard-type density-density interaction (Luttinger parameter $K$) that reduces the scaling dimension of the 3-4-5-0 interaction from $5$ to $5K$, making it relevant for $K<2/5$. Density-matrix renormalization group calculations show the opening of an excitation gap in this regime without the appearance of a degenerate ground state, the hallmark of symmetric mass generation.

hep-th↗

arXiv2026

Tangent fermions can restore vacuum stability of discrete-time Dirac models

The Dirac quantum walk (a 1+1 dimensional space-time discretization of the Dirac equation) has a $2μ$ mass gap both at the center and at the corner of the quasi-energy-momentum Brillouin zone. Gupta and Short recently noted [Quantum 9, 1845 (2025)] that the Dirac vacuum can create a particle-hole pair at the zone corner with the release of an energy $2μ$ to the environment. They removed this vacuum instability at the expense of fermion doubling, the appearance of a second low-energy Dirac cone. Here we show that an alternative discretization scheme, with a tangent rather than a sine dispersion relation, offers stability while retaining a single Dirac cone. The key step is the Cayley transformation from the unit circle of Floquet eigenvalues $e^{-i\varepsilon}$ to the real line of unbounded energies $E=2\tan(\varepsilon/2)$. We compute the Schwinger effect (particle-hole pair creation in a uniform electric field) for tangent fermions and show that the pair-production rate agrees with the continuum result for a single Dirac cone. The zone corner is exactly decoupled if the scalar potential is coupled through the Hermitian generator of the quantum map. If it is coupled as a split operator, in order to preserve exact gauge invariance on the lattice, the corner does contribute - with a weight that vanishes quadratically with the lattice constants, in contrast to the Dirac quantum walk where the zone-corner instability survives the continuum limit.

quant-ph↗

arXiv2026

Fragile single-cone Dirac quantum walks in two dimensions

It is known that a one-dimensional (1D) quantum walk gives a local space-time discretization of the massless Dirac equation with a single quasi-energy cone (no fermion doubling at low energies), keeping the fundamental symmetries (chiral and time-reversal) of the continuum theory. We show that the analogous 2D construction is fundamentally more fragile. Local two-band quantum walks can have an unpaired Dirac cone, but the protecting symmetries then cease to be ordinary on-site symmetries: They become non-symmorphic, involving half-lattice translations, and are broken by generic spatial inhomogeneities. In particular, we demonstrate that the 2D Dirac quantum walk based on the Ho-Chalker network model can be gapped by potential scattering, as is evidenced by the breakdown of reflectionless Klein tunneling. The symmorphic symmetry obstruction is sharp: If we allow for couplings that are no longer strictly finite-range but decay exponentially with distance, we can construct a 2D quantum walk with a single Dirac cone and on-site chiral and time-reversal symmetries.

quant-ph↗

arXiv2026

Monitored chaotic scattering

We extend the random-matrix theory of chaotic scattering to quantum dots whose dynamics is monitored by time-resolved measurements. Starting from a scattering matrix drawn from a circular ensemble, we construct the corresponding ensemble of Kraus operators for the monitored evolution of the many-body density matrix. In the single-particle sector the sum over measurement outcomes can be carried out algebraically, giving a discrete-time quantum master equation for the transferred charge. We solve this equation numerically and compare the resulting charge-transfer statistics with closed-form random-matrix predictions. The latter rely on an equipartition rule for monitored particles, which we formulate as a conjecture and test against the master equation.

cond-mat.mes-hall↗

arXiv2026

Quantum circuit decomposition of the tangent-fermion Dirac operator

The Dirac operator on a lattice cannot be both local and free of fermion doubling, at least not without breaking fundamental symmetries. Non-local, symmetry-preserving discretizations that avoid doubling have a quantum circuit representation as a linear-combination-of-unitaries (LCU) in which both the number of terms and their norm (the subnormalization factor) grow with the lattice size, compromising the efficiency of a quantum algorithm. We show that the tangent-fermion discretization escapes this obstruction when the Dirac equation is written as a generalized eigenvalue problem with a local operator pencil: Each member of the pencil has an exact LCU, with term count that is independent of lattice size and with subnormalization factor of order unity, on a par with elliptic operators. This provides an efficient block-encoding primitive for Dirac spectra and Green functions without fermion doubling.

quant-ph↗

arXiv2026

Monitored quantum transport through a disordered one-dimensional conductor

We formulate a quantum master equation for the many-particle density matrix of electrons propagating through a single-mode conductor, combining elastic scattering by disorder with time-resolved projective measurements that monitor the outcome of scattering events. The full counting statistics of transmitted electrons has a binomial distribution function, whose mean ${\cal T}$ and variance ${\cal T}(1-{\cal T})$ determine the conductance and shot noise power, respectively. Monitoring suppresses the phase coherence responsible for one-dimensional localization: The decay with conductor length $L$ of the typical transmission probability crosses over at $L\simeq \ell_ϕ$ from the exponential $e^{-L/ξ}$ (with localization length $ξ$) to the Ohmic $1/L$ decay. Numerical solution of the master equation gives, for weak monitoring, a logarithmic dependence $\ell_ϕ\simeq ξ\ln(v_{\rm F}τ_ϕ/ξ)$ of the coherence length $\ell_ϕ$ on the mean time $τ_ϕ$ between measurements.

cond-mat.mes-hall↗

arXiv2026

Lattice fermion simulation of spontaneous time-reversal symmetry breaking in a helical Luttinger liquid

We extend a recently developed "tangent fermion" method to discretize the Hamiltonian of a helical Luttinger liquid on a one-dimensional lattice, including two-particle backscattering processes that may open a gap in the spectrum. The fermion-doubling obstruction of the sine dispersion is avoided by working with a tangent dispersion, preserving the time-reversal symmetry of the Hamiltonian. The numerical results from a tensor network calculation on a finite lattice confirm the expectation from infinite-system analytics, that a gapped phase with spontaneously broken time-reversal symmetry emerges when the Fermi level is tuned to the Dirac point and the Luttinger parameter crosses a critical value.

cond-mat.str-el↗

arXiv2025

Pure dephasing increases partition noise in the quantum Hall effect

Quantum Hall edge channels partition electric charge over N chiral (uni-directional) modes. Intermode scattering leads to partition noise, observed in graphene p-n junctions. While inelastic scattering suppresses this noise by averaging out fluctuations, we show that pure (quasi-elastic) dephasing may enhance the partition noise. The noise power increases by up to 50% for two modes, with a general enhancement factor of 1+1/N in the strong-dephasing limit. This counterintuitive effect is explained in the framework of monitored quantum transport, arising from the self-averaging of quantum trajectories.

cond-mat.mes-hall↗

arXiv2025

Monitored quantum transport: full counting statistics of a quantum Hall interferometer

We generalize the Levitov-Lesovik formula for the probability distribution function of the electron charge transferred through a phase coherent conductor, to include projective measurements that monitor the chiral propagation in quantum Hall edge modes. When applied to an electronic Mach-Zehnder interferometer, the monitoring reduces the visibility of the Aharonov-Bohm conductance oscillations while preserving the binomial form of the counting statistics, thereby removing a fundamental shortcoming of the dephasing-probe model of decoherence.

cond-mat.mes-hall↗

arXiv2025

Helical Luttinger liquid on a space-time lattice

The Luttinger model is a paradigm for the breakdown due to interactions of the Fermi liquid description of one-dimensional massless Dirac fermions. Attempts to discretize the model on a one-dimensional lattice have failed to reproduce the established bosonization results, because of the fermion-doubling obstruction: A local and symmetry-preserving discretization of the Hamiltonian introduces a spurious second species of low-energy excitations, while a nonlocal discretization opens a single-particle gap at the Dirac point. Here we show how to work around this obstruction, by discretizing both space and time to obtain a \textit{local} Lagrangian for a helical Luttinger liquid with Hubbard interaction. The approach enables quantum Monte Carlo simulations that preserve the topological protection of an unpaired Dirac cone.

cond-mat.str-el↗

arXiv2025

Bimodal distribution of delay times and splitting of the zero-bias conductance peak in a double-barrier normal-superconductor junction

We formulate a scattering theory of the proximity effect in a weakly disordered SININ junction (S = superconductor, I = insulating barrier, N = normal metal). This allows to relate the conductance and density of states of the junction to the scattering times $τ$ (eigenvalues of the Wigner-Smith time-delay matrix). The probability density $P(τ)$ has two peaks, at a short time $τ_{\rm min}$ and a late time $τ_{\rm max}$. The density of states at the Fermi level is the geometric mean of the two times. The splitting of the zero-bias conductance peak is given by $\hbar/τ_{\rm max}$.

cond-mat.mes-hall↗

arXiv2025

Shot noise from which-path detection in a chiral Majorana interferometer

We calculate the full counting statistics of charge transfer in a chiral Majorana interferometer - a setup where a Dirac mode (an electron-hole mode) is split into two Majorana modes that encircle a number of h/2e vortices in a topological superconductor. Without any coupling to the environment it is known that the low-energy charge transfer is deterministic: An electron is transferred either as an electron or as a hole, dependent on the parity of the vortex number. We show that a stochastic contribution appears if which-path information leaks into the environment, producing the shot noise of random 2e charge transfers with binomial statistics. The Fano factor (dimensionless ratio of shot noise power and conductance) increases without bound as the which-path detection probability tends to unity.

cond-mat.mes-hall↗

arXiv2025

Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice

The massless two-dimensional Dirac equation in a perpendicular magnetic field B supports a B-independent "zeroth Landau level", a dispersionless zero-energy-mode protected by chiral symmetry. On a lattice the zero-mode becomes doubly degenerate with states of opposite chirality, which removes the protection and allows for a broadening when the magnetic field is non-uniform. It is known that this fundamental obstruction can be avoided by spatially separating the doubly degenerate states, adjoining +B and -B regions in a system of twice the size. Here we show that the same objective can be achieved without doubling the system size. The key ingredients are 1) a chirality-preserving "tangent fermion" discretization of the Dirac equation; and 2) a boundary condition that ensures the zero-mode contains only states of a single chirality.

cond-mat.mes-hall↗

arXiv2025

Majorana-metal transition in a disordered superconductor: percolation in a landscape of topological domain walls

Most superconductors are thermal insulators. A disordered chiral $\textit{p}$-wave superconductor, however, can make a transition to a thermal metal phase. Because heat is then transported by Majorana fermions, this phase is referred to as a Majorana metal. Here we present numerical evidence that the mechanism for the phase transition with increasing electrostatic disorder is the percolation of boundaries separating domains of different Chern number. We construct the network of domain walls using the spectral localizer as a ``topological landscape function'', and obtain the thermal metal--insulator phase diagram from the percolation transition.

cond-mat.mes-hall↗

arXiv2025

Entropy and singular-value moments of products of truncated random unitary matrices

Products of truncated unitary matrices, independently and uniformly drawn from the unitary group, can be used to study universal aspects of monitored quantum circuits. The von Neumann entropy of the corresponding density matrix decreases with increasing length $L$ of the product chain, in a way that depends on the matrix dimension $N$ and the truncation depth $δN$. Here we study that dependence in the double-scaling limit $L,N\rightarrow\infty$, at fixed ratio $τ=LδN/N$. The entropy reduction crosses over from a linear to a logarithmic dependence on $τ$ when this parameter crosses unity. The central technical result is an expression for the singular-value moments of the matrix product in terms of the Erlang function from queueing theory.

quant-ph↗

arXiv2024

Repulsive Casimir force from a Majorana zero-mode

Fu and Kane have taught us that a Majorana zero-mode appears on the quantum spin Hall edge at the interface with a superconductor. If a magnetic scatterer is placed on the edge, the zero-point energy of massless edge excitations exerts a force on the scatterer. This is the fermionic analogue of the electromagnetic Casimir effect. We show that the Majorana zero-mode produces a repulsive Casimir force, pushing the scatterer away from the superconductor. Unlike some other signatures of Majorana zero-modes, the repulsive Casimir force is directly tied to the topological invariant of the system (the sign of the determinant of the reflection matrix from the superconductor).

cond-mat.mes-hall↗

arXiv2024

Poor-man's Majorana edge mode enabled by specular Andreev reflection

It is known that the surface of a three-dimensional topological insulator (3D TI) supports a chiral Majorana edge mode at the interface between a superconductor and a magnetic insulator. The complexity of the materials combination is such that this state has not yet been observed. Here we show that a helical Majorana edge mode appears even in the absence of the magnetic insulator, if the Fermi level of the massless surface electrons is at the Dirac point. Specular Andreev reflection of Dirac fermions is at the origin of the effect. The simplified geometry may favor experimental observation of the helical Majorana mode, although it lacks the topological protection of its chiral counterpart.

cond-mat.mes-hall↗