Abstract As the desire to explore opaque materials is ordinarily frustrated by multiple scattering of waves, attention has focused on transmission matrix wave field. This gives fullest account and conductance enables control transmitted flux; however, it cannot address fundamental issue spatial profile eigenchannels inside sample. Here we obtain a universal expression for average disposition energy within random diffusive systems in terms auxiliary localization lengths determined...

Abstract Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation. However, high sensitivity of qubits environmental interference and error rates in current quantum devices exceed correction thresholds required for effective algorithm execution. Therefore, technology is crucial achieving reliable computing. In this work, we study a topological surface code with two-dimensional lattice structure, which protects information...

<title>Abstract</title> To address qubits' high environmental sensitivity and reduce the significant error rates in current quantum devices, correction stands as one of most dependable approaches. The topological surface code, renowned for its unique qubit lattice structure, is widely considered a pivotal tool enabling fault-tolerant computation. Through redundancy introduced across multiple qubits, code safeguards information identifies errors via state changes captured by syndrome qubits....

We present the first microscopic theory of transport in quasiperiodically driven environments (``kicked rotors''), as realized recent atom optic experiments. find that behavior these systems depends sensitively on value a dimensionless Planck constant $\stackrel{\texttildelow{}}{h}$: for irrational values $\stackrel{\texttildelow{}}{h}/(4\ensuremath{\pi})$ they fall into universality class disordered electronic and we describe corresponding localization phenomena. In contrast, rational...

We report a first-principles study of static transport localized waves in quasi-one-dimensional open media. found that such transport, dominated by disorder-induced resonant transmissions, displays novel diffusive behavior. Our analytical predictions are entirely confirmed numerical simulations. showed the prevailing self-consistent localization theory [van Tiggelen, {\it et. al.}, Phys. Rev. Lett. \textbf{84}, 4333 (2000)] is valid only if transmissions negligible. findings new direction Anderson

We find in a canonical chaotic system, the kicked spin-1/2 rotor, Planck's quantum(he)-driven phenomenon bearing close analogy to integer quantum Hall effect but of chaos origin. Specifically, rotor's energy growth is unbounded ("metallic" phase) for discrete set critical values he, otherwise bounded ("insulating" phase). The latter phase topological and characterized by number ("quantized conductance"). jumps unity whenever he passes through each value as it decreases. Our findings indicate...

A supersymmetric field theory of light diffusion in semi-infinite disordered media is presented. With the help this technique we justify---at perturbative level---the local proposed by Tiggelen, Lagendijk, and Wiersma [Phys. Rev. Lett. 84, 4333 (2000)], show that coherent backscattering line shape medium bar displays a crossover from two-dimensional weak to quasi-one-dimensional strong localization.

We present an analytic theory of quantum interference and Anderson localization in the kicked rotor (QKR). The behavior system is known to depend sensitively on value its effective Planck's constant $\he$. here show that for rational values $\he/(4\pi)=p/q$, it bears similarity a disordered metallic ring circumference $q$ threaded by Aharonov-Bohm flux. Building correspondence, we obtain quantitative results time--dependent QKR kinetic energy, $E(\tilde t)$ (this observable which probes...

Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly the high ${T}_{c}$ cuprates. This conventionally understood terms of Hartree-Fock-type mean-field theory. Here we demonstrate a mechanism for charge modulation rooted many-particle quantum physics arising strong coupling limit. Specifically, consider problem single hole bipartite $t\text{\ensuremath{-}}J$ ladder. As remnant...

Quantum kicked rotor (QKR) is a standard model of chaos that describes particle moving on ring under time-modulated kicking. This paper demonstrates large class spin-$\frac{1}{2}$ quasiperiodic QKR models exhibits dynamical analog the integer quantum Hall effect, which usually associated with two-dimensional electronic systems. Additionally, authors reveal topological theta angle, fundamental concept in chromodynamics, can emerge models.

We report the first experimental observation of time-driven phase transition in a canonical quantum chaotic system, kicked rotor. The bears firm analogy to thermodynamic transition, with time mimicking temperature and expectation rotor's kinetic energy free energy. signals sudden change system's memory behavior: before critical time, system undergoes motion space its initial states is erased course time; after interference enhances probability for trajectory return state, thus recovered.

It is generally accepted that doped Mott insulators can be well characterized by the t-J model. In model, electron fractionalization dictated phase string effect. We found in underdoped regime, antiferromagnetic and superconducting phases are dual: former, holons confined while spinons deconfined, {\it vice versa} latter. These two separated a novel phase, so-called Bose-insulating where both deconfined. A pair of Wilson loops was to constitute complete set order parameters determining this...

In the $t-J$ model, electron fractionalization is unique due to non-perturbative phase string effect. We formulated a lattice field theory taking this effect into full account. Basing on theory, we introduced pair of Wilson loops which constitute complete set order parameters determining diagram in underdoped regime. also established general composition rule for electric transport expressing conductivity terms spinon and holon conductivities. The applied studies quantum diagram. found that...

Quantum kicked rotor was recently realized in experiments with cold atomic gases and standing optical waves. As predicted, it exhibits dynamical localization the momentum space. Here we consider weak-localization regime concentrating on Ehrenfest time scale. The latter accounts for spread of a minimal wave packet is proportional to logarithm Planck constant. We show that onset essentially delayed by four times, give quantitative predictions suitable an experimental verification.

The fate of a hole injected in an antiferromagnet is outstanding issue strongly correlated physics. It provides important insights into doped Mott insulators closely related to high-temperature superconductivity. Here, we report systematic numerical study t-J ladder systems based on the density matrix renormalization group. reveals surprising result for single hole's motion otherwise well-understood undoped system. Specifically, find that common belief quasiparticle picture invalidated by...

The quantum kicked rotor (QKR) is known to exhibit dynamical localization in the space of its angular momentum. present paper devoted systematic first--principal (without a regularizer) diagrammatic calculations weak--localization corrections for QKR. Our particular emphasis on Ehrenfest time regime -- phenomena characteristic classical--to--quantum crossover classically chaotic systems.

Transmission eigenchannels and associated eigenvalues, that give a full account of wave propagation in random media, have recently emerged as major theme theoretical applied optics. Here we demonstrate, both analytically numerically, quasi one-dimensional ($1$D) diffusive samples, their behavior is governed mostly by the asymmetry reflections sample edges rather than absolute values reflection coefficients themselves. We show there exists threshold value parameter, below which high...

The impact of surface reflection on the statistics transmission eigenvalues is a largely unexplored subject fundamental and practical importance in statistical optics. Here, we develop first-principles theory confirm numerically that distribution diffusive waves exhibits nonanalytic transition as strength at one passes through critical value while other fixed. Above value, highest eigenvalue strictly smaller than unity decreases with increasing internal reflection. When input output surfaces...

Disorder is more the rule than exception in natural and synthetic materials. Nonetheless, wave propagation within inhomogeneously disordered materials has received scant attention. We combine microwave experiments theory to find spatial variation of generic quantities demonstrate that statistics samples any dimension are independent detailed structure a material depend only on net strengths distributed scattering reflection between observation point each boundaries.

Abstract Understanding fluctuation phenomena plays a dominant role in the development of many-body physics. The time evolution entanglement is essential to broad range subjects physics, ranging from exotic quantum matter thermalization. Stemming various dynamical processes information, fluctuations differ conceptually out-of-equilibrium traditional physical quantities. Their studies remain elusive. Here we uncover an emergent random structure wavefunction two classes integrable—either...

We study the crossover from a classical to quantum picture in electron energy statistics system with broken time-reversal symmetry. The perturbative and nonperturbative parts of two level correlation function $R(\ensuremath{\omega})$ are analyzed. find that intermediate region $\mathrm{\ensuremath{\Delta}}⪡\ensuremath{\omega}\ensuremath{\sim}{t}_{E}^{\ensuremath{-}1}⪡{t}_{\mathrm{erg}}^{\ensuremath{-}1}$, where ${t}_{E}$ ${t}_{\mathrm{erg}}$ Ehrenfest ergodic times, respectively, consists...

We study Anderson localization in quasi--one--dimensional disordered wires within the framework of replica $\sigma$--model. Applying a semiclassical approach (geodesic action plus Gaussian fluctuations) recently introduced context supersymmetry by Lamacraft, Simons and Zirnbauer \cite{LSZ}, we compute {\em exact} density transmission matrix eigenvalues superconducting (of symmetry class $C$I.) For unitary metallic systems (class $A$) are able to obtain function, save for its large tail.

We calculate the Ehrenfest-time dependence of leading quantum correction to spectral form factor a ballistic chaotic cavity using periodic orbit theory. For case broken time-reversal symmetry, when involves two small-angle encounters classical trajectories, our result differs from that previously obtained field-theoretic methods [Tian and Larkin, Phys. Rev. B 70, 035305 (2004)]. While we believe existing calculation is technically flawed, question whether field theoretic periodic-orbit...