The fate of a hole injected in an antiferromagnet is an outstanding issue of strongly correlated physics. It provides important insights into doped Mott insulators closely related to high-temperature superconductivity. Here, we report a systematic numerical study of t-J ladder systems based on the density matrix renormalization group. It reveals a surprising result for the single hole's motion in an otherwise well-understood undoped system. Specifically, we find that the common belief of quasiparticle picture is invalidated by the self-localization of the doped hole. In contrast to Anderson localization caused by disorders, the charge localization discovered here is an entirely new phenomenon purely of strong correlation origin. It results from destructive quantum interference of novel signs picked up by the hole, and since the same effect is of a generic feature of doped Mott physics, our findings unveil a new paradigm which may go beyond the single hole doped system.

PurposeIn cancer patients, tumor gene mutations contribute to drug resistance and treatment failure. In patients with metastatic breast cancer (MBC), these mutations increase after multiline treatment, thereby decreasing treatment efficiency. The aim of this study was to evaluate gene mutation patterns in MBC patients to predict drug resistance and disease progression.MethodA total of 68 MBC patients who had received multiline treatment were recruited. Circulating tumor DNA (ctDNA) mutations were evaluated and compared among hormone receptor (HR)/human epidermal growth factor receptor 2 (HER2) subgroups.ResultsThe baseline gene mutation pattern (at the time of recruitment) varied among HR/HER2 subtypes. BRCA1 and MED12 were frequently mutated in triple negative breast cancer (TNBC) patients, PIK3CA and FAT1 mutations were frequent in HR+ patients, and PIK3CA and ERBB2 mutations were frequent in HER2+ patients. Gene mutation patterns also varied in patients who progressed within either 3 months or 3–6 months of chemotherapy treatment. For example, in HR+ patients who progressed within 3 months of treatment, the frequency of TERT mutations significantly increased. Other related mutations included FAT1 and NOTCH4. In HR+ patients who progressed within 3–6 months, PIK3CA, TP53, MLL3, ERBB2, NOTCH2, and ERS1 were the candidate mutations. This suggests that different mechanisms underlie disease progression at different times after treatment initiation. In the COX model, the ctDNA TP53 + PIK3CA gene mutation pattern successfully predicted progression within 6 months.ConclusionctDNA gene mutation profiles differed among HR/HER2 subtypes of MBC patients. By identifying mutations associated with treatment resistance, we hope to improve therapy selection for MBC patients who received multiline treatment.

As the desire to explore opaque materials is ordinarily frustrated by multiple scattering of waves, attention has focused on the transmission matrix of the wave field. This matrix gives the fullest account of transmission and conductance and enables the control of the transmitted flux; however, it cannot address the fundamental issue of the spatial profile of eigenchannels of the transmission matrix inside the sample. Here we obtain a universal expression for the average disposition of energy of transmission eigenchannels within random diffusive systems in terms of auxiliary localization lengths determined by the corresponding transmission eigenvalues. The spatial profile of each eigenchannel is shown to be a solution of a generalized diffusion equation. These results reveal the rich structure of transmission eigenchannels and enable the control of the energy distribution inside random media.

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

Abstract. We present an analytic theory of quantum interference and Anderson localization in the quantum kicked rotor (QKR). The behavior of the system is known to depend sensitively on the value of its effective Planck's constant,h. We show here that for rational values ofh/(4π) = p/q, it bears a similarity to a disordered metallic ring of circumference q and threaded by an Aharonov-Bohm flux. Building on this correspondence, we obtain quantitative results for the timedependent behavior of the QKR kinetic energy, E(t) (this is an observable that sensitively probes the system's localization properties). For values of q smaller than the localization length ξ , we obtain scaling E(t) ∼ t 2 , where = 2π/q is the quasi-energy level spacing on the ring. This scaling is indicative of a long time dynamics that is neither localized nor diffusive. For larger values q ξ , the functions E(t) → ξ 2 saturate (up to exponentially small corrections ∼ exp(−q/ξ )), thus reflecting essentially localized behavior.

We present the first microscopic theory of transport in quasiperiodically driven environments ("kicked rotors"), as realized in recent atom optic experiments. We find that the behavior of these systems depends sensitively on the value of a dimensionless Planck constant h: for irrational values of h/(4π) they fall into the universality class of disordered electronic systems and we describe the corresponding localization phenomena. In contrast, for rational values the rotor-Anderson insulator acquires an infinite (static) conductivity and turns into a "supermetal." We discuss the ensuing possibility of a metal-supermetal quantum phase transition.

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

Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly in the high Tc cuprates. This phenomenon is conventionally understood in terms of Hartree-Fock type mean field theory. Here we demonstrate a new mechanism for charge modulation which is rooted in the many-particle quantum physics arising in the strong coupling limit. Specifically, we consider the problem of a single hole in a bipartite t − J ladder. As a remnant of the fermion signs, the hopping hole picks up subtle phases pending the fluctuating spins, the so-called phase string effect. We demonstrate the presence of charge modulations in the density matrix renormalization group solutions which disappear when the phase strings are switched off. This new form of charge modulation can be understood analytically in a path-integral language with a mean-field like approximation adopted, showing that the phase strings give rise to constructive interferences leading to self-localization. When the latter occurs, left-and right-moving propagating modes emerge inside the localization volume and their interference is responsible for the real space charge modulation.