KPZ equation in one dimension and line ensembles

For suitably discretized versions of the Kardar-Parisi-Zhang equation in one space dimension exact scaling functions are available, amongst them the stationary two-point function. We explain one central piece from the technology through which such results are obtained, namely the method of line ensembles with purely entropic repulsion.Comment: Proceedings STATPHYS22, Bangalore, 200

Polynuclear growth model, GOE2^2 and random matrix with deterministic source

We present a random matrix interpretation of the distribution functions which have appeared in the study of the one-dimensional polynuclear growth (PNG) model with external sources. It is shown that the distribution, GOE$^2$, which is defined as the square of the GOE Tracy-Widom distribution, can be obtained as the scaled largest eigenvalue distribution of a special case of a random matrix model with a deterministic source, which have been studied in a different context previously. Compared to the original interpretation of the GOE$^2$ as ``the square of GOE'', ours has an advantage that it can also describe the transition from the GUE Tracy-Widom distribution to the GOE$^2$. We further demonstrate that our random matrix interpretation can be obtained naturally by noting the similarity of the topology between a certain non-colliding Brownian motion model and the multi-layer PNG model with an external source. This provides us with a multi-matrix model interpretation of the multi-point height distributions of the PNG model with an external source.Comment: 27pages, 4 figure

Enviromental Implications of Växjö Municipality's Energy Requirement for New Residential Buildings

AbstractThe Växjö Municipality in Sweden sets specific energy requirements above the national building code while selling land for new residential buildings. A main energy requirement for Östra Lugnet residential area in Växjö was that all buildings must be connected to the district heating network. In this paper we analysed final energy use of the buildings, and compared the primary energy use and CO2 emission from operation of the buildings connected to district heating system with hypothetical scenarios where only air-source heat pumps were installed. The result showed that district heating is the better option from the perspective of lower carbon emission. Therefore, it seems appropriate for Växjö Municipality to set conditions for new residential buildings in Östra Lugnet to connect to the local district heating network as it contributes to its goal of low carbon society

On the stability of quantum holonomic gates

We provide a unified geometrical description for analyzing the stability of holonomic quantum gates in the presence of imprecise driving controls (parametric noise). We consider the situation in which these fluctuations do not affect the adiabatic evolution but can reduce the logical gate performance. Using the intrinsic geometric properties of the holonomic gates, we show under which conditions on noise's correlation time and strength, the fluctuations in the driving field cancel out. In this way, we provide theoretical support to previous numerical simulations. We also briefly comment on the error due to the mismatch between real and nominal time of the period of the driving fields and show that it can be reduced by suitably increasing the adiabatic time.Comment: 7 page

Average characteristic polynomials in the two-matrix model

The two-matrix model is defined on pairs of Hermitian matrices $(M_1,M_2)$ of size $n\times n$ by the probability measure $$\frac{1}{Z_n} \exp\left(\textrm{Tr} (-V(M_1)-W(M_2)+\tau M_1M_2)\right)\ dM_1\ dM_2,$$ where $V$ and $W$ are given potential functions and \tau\in\er. We study averages of products and ratios of characteristic polynomials in the two-matrix model, where both matrices $M_1$ and $M_2$ may appear in a combined way in both numerator and denominator. We obtain determinantal expressions for such averages. The determinants are constructed from several building blocks: the biorthogonal polynomials $p_n(x)$ and $q_n(y)$ associated to the two-matrix model; certain transformed functions $\P_n(w)$ and \Q_n(v); and finally Cauchy-type transforms of the four Eynard-Mehta kernels $K_{1,1}$, $K_{1,2}$, $K_{2,1}$ and $K_{2,2}$. In this way we generalize known results for the $1$-matrix model. Our results also imply a new proof of the Eynard-Mehta theorem for correlation functions in the two-matrix model, and they lead to a generating function for averages of products of traces.Comment: 28 pages, references adde

Prospects for cooling nanomechanical motion by coupling to a superconducting microwave resonator

Recent theoretical work has shown that radiation pressure effects can in principle cool a mechanical degree of freedom to its ground state. In this paper, we apply this theory to our realization of an opto-mechanical system in which the motion of mechanical oscillator modulates the resonance frequency of a superconducting microwave circuit. We present experimental data demonstrating the large mechanical quality factors possible with metallic, nanomechanical beams at 20 mK. Further measurements also show damping and cooling effects on the mechanical oscillator due to the microwave radiation field. These data motivate the prospects for employing this dynamical backaction technique to cool a mechanical mode entirely to its quantum ground state.Comment: 6 pages, 6 figure

The effect of mindfulness group therapy on a broad range of psychiatric symptoms : A randomised controlled trial in primary health care

Background The need for psychotherapy in primary health care is on the increase but individual-based treatment is costly. The main aim of this randomised controlled trial (RCT) was to compare the effect of mindfulness-based group therapy (MGT) with treatment as usual (TAU), mainly individual-based cognitive behavioural therapy (CBT), on a broad range of psychiatric symptoms in primary care patients diagnosed with depressive, anxiety and/or stress and adjustment disorders. An additional aim was to compare the effect of MGT with TAU on mindful attention awareness. Methods This 8-week RCT took place in 2012 at 16 primary care centres in southern Sweden. The study population included both men and women, aged 20–64 years (n = 215). A broad range of psychiatric symptoms were evaluated at baseline and at the 8-week follow-up using the Symptom Checklist-90 (SCL-90). Mindful attention awareness was also evaluated using the Mindful Attention Awareness Scale (MAAS). Results In both groups, the scores decreased significantly for all subscales and indexes in SCL-90, while the MAAS scores increased significantly. There were no significant differences in the change in psychiatric symptoms between the two groups. The mindfulness group had a somewhat larger change in scores than the control group on the MAAS (P = 0.06, non-significant). Conclusions No significant differences between MGT and TAU, mainly individual-based CBT, were found in treatment effect. Both types of therapies could be used in primary care patients with depressive, anxiety and/or stress and adjustment disorders, where MGT has a potential to save limited resources. Trial registration ClinicalTrials.gov identifier: NCT01476371

Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in TASEP with the step-type initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of TASEP to the Schur process, we show that the function is represented as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources.Comment: 48 pages, 8 figure