Electrical transport quantum effects in the In0.53Ga0.47As/In0.52Al0.48As heterostructure on silicon

Electrical transport in a modulation doped heterostructure of In0.53Ga0.47As/In0.52Al0.48As grown on Si by molecular beam epitaxy has been measured. Quantum Hall effect and Subnikov¿De Haas oscillations were observed indicating the two¿dimensional character of electron transport. A mobility of 20¿000 cm2/V¿s was measured at 6 K for an electron sheet concentration of 1.7×1012 cm¿2. Transmission electron microscopy observations indicated a significant surface roughness and high defect density of the InGaAs/InAlAs layers to be present due to the growth on silicon. In addition, fine¿scale composition modulation present in the In0.53Ga0.47As/In0.52Al0.48As may further limit transport properties.

Intense green-yellow electroluminescence from Tb+-implanted silicon-rich silicon nitride/oxide light emitting devices

High optical power density of 0.5 mW/cm2, external quantum efficiency of 0.1%, and population inversion of 7% are reported from Tb+-implanted silicon-rich silicon nitride/oxide light emitting devices. Electrical and electroluminescence mechanisms in these devices were investigated. The excitation cross section for the 543 nm Tb3+ emission was estimated under electrical pumping, resulting in a value of 8.2 × 10−14 cm2, which is one order of magnitude larger than one reported for Tb3+:SiO2 light emitting devices. These results demonstrate the potentiality of Tb+-implanted silicon nitride material for the development of integrated light sources compatible with Si technology.

Energy transfer mechanism and Auger effect in Er3+ coupled silicon nanoparticle samples

We report a spectroscopic study about the energy transfer mechanism among silicon nanoparticles (Si-np), both amorphous and crystalline, and Er ions in a silicon dioxide matrix. From infrared spectroscopic analysis, we have determined that the physics of the transfer mechanism does not depend on the Si-np nature, finding a fast (< 200 ns) energy transfer in both cases, while the amorphous nanoclusters reveal a larger transfer efficiency than the nanocrystals. Moreover, the detailed spectroscopic results in the visible range here reported are essential to understand the physics behind the sensitization effect, whose knowledge assumes a crucial role to enhance the transfer rate and possibly employing the material in optical amplifier devices. Joining the experimental data, performed with pulsed and continuous-wave excitation, we develop a model in which the internal intraband recombination within Si-np is competitive with the transfer process via an Auger electron"recycling" effect. Posing a different light on some detrimental mechanism such as Auger processes, our findings clearly recast the role of Si-np in the sensitization scheme, where they are able to excite very efficiently ions in close proximity to their surface. (C) 2010 American Institute of Physics.

Asymptotic analysis of the Gunn effect with realistic boundary conditions

A general asymptotic analysis of the Gunn effect in n-type GaAs under general boundary conditions for metal-semiconductor contacts is presented. Depending on the parameter values in the boundary condition of the injecting contact, different types of waves mediate the Gunn effect. The periodic current oscillation typical of the Gunn effect may be caused by moving charge-monopole accumulation or depletion layers, or by low- or high-field charge-dipole solitary waves. A new instability caused by multiple shedding of (low-field) dipole waves is found. In all cases the shape of the current oscillation is described in detail: we show the direct relationship between its major features (maxima, minima, plateaus, etc.) and several critical currents (which depend on the values of the contact parameters). Our results open the possibility of measuring contact parameters from the analysis of the shape of the current oscillation.

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly established.

Raman scattering of InSb quantum dots grown on InP substrates

In this paper we present the Raman scattering of self-assembled InSb dots grown on (001) oriented InP substrates. The samples were grown by pulsed molecular beam epitaxy mode. Two types of samples have been investigated. In one type the InSb dots were capped with 200 monolayers of InP; in the other type no capping was deposited after the InSb dot formation. We observe two peaks in the Raman spectra of the uncapped dot, while only one peak is observed in the Raman spectra of the capped dots. In the case of the uncapped dots the peaks are attributed to LO-like and TO-like vibration of completely relaxed InSb dots, in agreement with high resolution transmission electron microscopy photographs. The Raman spectra of the capped dot suggest a different strain state in the dot due to the capping layer.

Multiple edges of a quantum Hall system in a strong electric

In this paper we show that if the electrons in a quantum Hall sample are subjected to a constant electric field in the plane of the material, comparable in magnitude to the background magnetic field on the system of electrons, a multiplicity of edge states localized at different regions of space is produced in the sample. The actions governing the dynamics of these edge states are obtained starting from the well-known Schrödinger field theory for a system of nonrelativistic electrons, where on top of the constant background electric and magnetic fields, the electrons are further subject to slowly varying weak electromagnetic fields. In the regions between the edges, dubbed as the "bulk," the fermions can be integrated out entirely and the dynamics expressed in terms of a local effective action involving the slowly varying electromagnetic potentials. It is further shown how the bulk action is gauge noninvariant in a particular way, and how the edge states conspire to restore the U(1) electromagnetic gauge invariance of the system. In the edge action we obtain a heretofore unnoticed gauge-invariant term that depends on the particular edge. We argue that this term may be detected experimentally as different edges respond differently to a monochromatic probe due to this term

Vertically coupled quantum dots in the local spin-density functional theory

We have investigated the structure of double quantum dots vertically coupled at zero magnetic field within local-spin-density functional theory. The dots are identical and have a finite width, and the whole system is axially symmetric. We first discuss the effect of thickness on the addition spectrum of one single dot. Next we describe the structure of coupled dots as a function of the interdot distance for different electron numbers. Addition spectra, Hund's rule, and molecular-type configurations are discussed. It is shown that self-interaction corrections to the density-functional results do not play a very important role in the calculated addition spectra

Dissociation of vertical semiconductor diatomic artificial molecules

We investigate the dissociation of few-electron circular vertical semiconductor double quantum dot artificial molecules at 0 T as a function of interdot distance. A slight mismatch introduced in the fabrication of the artificial molecules from nominally identical constituent quantum wells induces localization by offsetting the energy levels in the quantum dots by up to 2 meV, and this plays a crucial role in the appearance of the addition energy spectra as a function of coupling strength particularly in the weak coupling limit.

Assessment of the occurrence of nanoparticles in Swiss industry and evaluation of the appropriatenesss of the measurement devices to determine the workforce exposure

Abstract : The occupational health risk involved with handling nanoparticles is the probability that a worker will experience an adverse health effect: this is calculated as a function of the worker's exposure relative to the potential biological hazard of the material. Addressing the risks of nanoparticles requires therefore knowledge on occupational exposure and the release of nanoparticles into the environment as well as toxicological data. However, information on exposure is currently not systematically collected; therefore this risk assessment lacks quantitative data. This thesis aimed at, first creating the fundamental data necessary for a quantitative assessment and, second, evaluating methods to measure the occupational nanoparticle exposure. The first goal was to determine what is being used where in Swiss industries. This was followed by an evaluation of the adequacy of existing measurement methods to assess workplace nanopaiticle exposure to complex size distributions and concentration gradients. The study was conceived as a series of methodological evaluations aimed at better understanding nanoparticle measurement devices and methods. lt focused on inhalation exposure to airborne particles, as respiration is considered to be the most important entrance pathway for nanoparticles in the body in terms of risk. The targeted survey (pilot study) was conducted as a feasibility study for a later nationwide survey on the handling of nanoparticles and the applications of specific protection means in industry. The study consisted of targeted phone interviews with health and safety officers of Swiss companies that were believed to use or produce nanoparticles. This was followed by a representative survey on the level of nanoparticle usage in Switzerland. lt was designed based on the results of the pilot study. The study was conducted among a representative selection of clients of the Swiss National Accident Insurance Fund (SUVA), covering about 85% of Swiss production companies. The third part of this thesis focused on the methods to measure nanoparticles. Several pre- studies were conducted studying the limits of commonly used measurement devices in the presence of nanoparticle agglomerates, This focus was chosen, because several discussions with users and producers of the measurement devices raised questions about their accuracy measuring nanoparticle agglomerates and because, at the same time, the two survey studies revealed that such powders are frequently used in industry. The first preparatory experiment focused on the accuracy of the scanning mobility particle sizer (SMPS), which showed an improbable size distribution when measuring powders of nanoparticle agglomerates. Furthermore, the thesis includes a series of smaller experiments that took a closer look at problems encountered with other measurement devices in the presence of nanoparticle agglomerates: condensation particle counters (CPC), portable aerosol spectrometer (PAS) a device to estimate the aerodynamic diameter, as well as diffusion size classifiers. Some initial feasibility tests for the efficiency of filter based sampling and subsequent counting of carbon nanotubes (CNT) were conducted last. The pilot study provided a detailed picture of the types and amounts of nanoparticles used and the knowledge of the health and safety experts in the companies. Considerable maximal quantities (> l'000 kg/year per company) of Ag, Al-Ox, Fe-Ox, SiO2, TiO2, and ZnO (mainly first generation particles) were declared by the contacted Swiss companies, The median quantity of handled nanoparticles, however, was 100 kg/year. The representative survey was conducted by contacting by post mail a representative selection of l '626 SUVA-clients (Swiss Accident Insurance Fund). It allowed estimation of the number of companies and workers dealing with nanoparticles in Switzerland. The extrapolation from the surveyed companies to all companies of the Swiss production sector suggested that l'309 workers (95%-confidence interval l'073 to l'545) of the Swiss production sector are potentially exposed to nanoparticles in 586 companies (145 to l'027). These numbers correspond to 0.08% (0.06% to 0.09%) of all workers and to 0.6% (0.2% to 1.1%) of companies in the Swiss production sector. To measure airborne concentrations of sub micrometre-sized particles, a few well known methods exist. However, it was unclear how well the different instruments perform in the presence of the often quite large agglomerates of nanostructured materials. The evaluation of devices and methods focused on nanoparticle agglomerate powders. lt allowed the identification of the following potential sources of inaccurate measurements at workplaces with considerable high concentrations of airborne agglomerates: - A standard SMPS showed bi-modal particle size distributions when measuring large nanoparticle agglomerates. - Differences in the range of a factor of a thousand were shown between diffusion size classifiers and CPC/SMPS. - The comparison between CPC/SMPS and portable aerosol Spectrometer (PAS) was much better, but depending on the concentration, size or type of the powders measured, the differences were still of a high order of magnitude - Specific difficulties and uncertainties in the assessment of workplaces were identified: the background particles can interact with particles created by a process, which make the handling of background concentration difficult. - Electric motors produce high numbers of nanoparticles and confound the measurement of the process-related exposure. Conclusion: The surveys showed that nanoparticles applications exist in many industrial sectors in Switzerland and that some companies already use high quantities of them. The representative survey demonstrated a low prevalence of nanoparticle usage in most branches of the Swiss industry and led to the conclusion that the introduction of applications using nanoparticles (especially outside industrial chemistry) is only beginning. Even though the number of potentially exposed workers was reportedly rather small, it nevertheless underscores the need for exposure assessments. Understanding exposure and how to measure it correctly is very important because the potential health effects of nanornaterials are not yet fully understood. The evaluation showed that many devices and methods of measuring nanoparticles need to be validated for nanoparticles agglomerates before large exposure assessment studies can begin. Zusammenfassung : Das Gesundheitsrisiko von Nanopartikel am Arbeitsplatz ist die Wahrscheinlichkeit dass ein Arbeitnehmer einen möglichen Gesundheitsschaden erleidet wenn er diesem Stoff ausgesetzt ist: sie wird gewöhnlich als Produkt von Schaden mal Exposition gerechnet. Für eine gründliche Abklärung möglicher Risiken von Nanomaterialien müssen also auf der einen Seite Informationen über die Freisetzung von solchen Materialien in die Umwelt vorhanden sein und auf der anderen Seite solche über die Exposition von Arbeitnehmenden. Viele dieser Informationen werden heute noch nicht systematisch gesarnmelt und felilen daher für Risikoanalysen, Die Doktorarbeit hatte als Ziel, die Grundlagen zu schaffen für eine quantitative Schatzung der Exposition gegenüber Nanopartikel am Arbeitsplatz und die Methoden zu evaluieren die zur Messung einer solchen Exposition nötig sind. Die Studie sollte untersuchen, in welchem Ausmass Nanopartikel bereits in der Schweizer Industrie eingesetzt werden, wie viele Arbeitnehrner damit potentiel] in Kontakt komrrien ob die Messtechnologie für die nötigen Arbeitsplatzbelastungsmessungen bereits genügt, Die Studie folcussierte dabei auf Exposition gegenüber luftgetragenen Partikel, weil die Atmung als Haupteintrittspforte iïlr Partikel in den Körper angesehen wird. Die Doktorarbeit besteht baut auf drei Phasen auf eine qualitative Umfrage (Pilotstudie), eine repräsentative, schweizerische Umfrage und mehrere technische Stndien welche dem spezitischen Verständnis der Mëglichkeiten und Grenzen einzelner Messgeräte und - teclmikeri dienen. Die qualitative Telephonumfrage wurde durchgeführt als Vorstudie zu einer nationalen und repräsentativen Umfrage in der Schweizer Industrie. Sie zielte auf Informationen ab zum Vorkommen von Nanopartikeln, und den angewendeten Schutzmassnahmen. Die Studie bestand aus gezielten Telefoninterviews mit Arbeit- und Gesundheitsfachpersonen von Schweizer Unternehmen. Die Untemehmen wurden aufgrund von offentlich zugànglichen lnformationen ausgewählt die darauf hinwiesen, dass sie mit Nanopartikeln umgehen. Der zweite Teil der Dolctorarbeit war die repräsentative Studie zur Evalniernng der Verbreitnng von Nanopaitikelanwendungen in der Schweizer lndustrie. Die Studie baute auf lnformationen der Pilotstudie auf und wurde mit einer repräsentativen Selektion von Firmen der Schweizerischen Unfall Versicherungsanstalt (SUVA) durchgeüihxt. Die Mehrheit der Schweizerischen Unternehmen im lndustrieselctor wurde damit abgedeckt. Der dritte Teil der Doktorarbeit fokussierte auf die Methodik zur Messung von Nanopartikeln. Mehrere Vorstudien wurden dnrchgefîihrt, um die Grenzen von oft eingesetzten Nanopartikelmessgeräten auszuloten, wenn sie grösseren Mengen von Nanopartikel Agglomeraten ausgesetzt messen sollen. Dieser F okns wurde ans zwei Gründen gewählt: weil mehrere Dislcussionen rnit Anwendem und auch dem Produzent der Messgeràte dort eine Schwachstelle vermuten liessen, welche Zweifel an der Genauigkeit der Messgeräte aufkommen liessen und weil in den zwei Umfragestudien ein häufiges Vorkommen von solchen Nanopartikel-Agglomeraten aufgezeigt wurde. i Als erstes widmete sich eine Vorstndie der Genauigkeit des Scanning Mobility Particle Sizer (SMPS). Dieses Messgerät zeigte in Präsenz von Nanopartikel Agglorneraten unsinnige bimodale Partikelgrössenverteilung an. Eine Serie von kurzen Experimenten folgte, welche sich auf andere Messgeräte und deren Probleme beim Messen von Nanopartikel-Agglomeraten konzentrierten. Der Condensation Particle Counter (CPC), der portable aerosol spectrometer (PAS), ein Gerät zur Schàtzung des aerodynamischen Durchniessers von Teilchen, sowie der Diffusion Size Classifier wurden getestet. Einige erste Machbarkeitstests zur Ermittlnng der Effizienz von tilterbasierter Messung von luftgetragenen Carbon Nanotubes (CNT) wnrden als letztes durchgeiührt. Die Pilotstudie hat ein detailliiertes Bild der Typen und Mengen von genutzten Nanopartikel in Schweizer Unternehmen geliefert, und hat den Stand des Wissens der interviewten Gesundheitsschntz und Sicherheitsfachleute aufgezeigt. Folgende Typen von Nanopaitikeln wurden von den kontaktierten Firmen als Maximalmengen angegeben (> 1'000 kg pro Jahr / Unternehrnen): Ag, Al-Ox, Fe-Ox, SiO2, TiO2, und ZnO (hauptsächlich Nanopartikel der ersten Generation). Die Quantitäten von eingesetzten Nanopartikeln waren stark verschieden mit einem ein Median von 100 kg pro Jahr. ln der quantitativen Fragebogenstudie wurden l'626 Unternehmen brieflich kontaktiert; allesamt Klienten der Schweizerischen Unfallversicherringsanstalt (SUVA). Die Resultate der Umfrage erlaubten eine Abschätzung der Anzahl von Unternehmen und Arbeiter, welche Nanopartikel in der Schweiz anwenden. Die Hochrechnung auf den Schweizer lndnstriesektor hat folgendes Bild ergeben: ln 586 Unternehmen (95% Vertrauensintervallz 145 bis 1'027 Unternehmen) sind 1'309 Arbeiter potentiell gegenüber Nanopartikel exponiert (95%-Vl: l'073 bis l'545). Diese Zahlen stehen für 0.6% der Schweizer Unternehmen (95%-Vl: 0.2% bis 1.1%) und 0.08% der Arbeiternehmerschaft (95%-V1: 0.06% bis 0.09%). Es gibt einige gut etablierte Technologien um die Luftkonzentration von Submikrometerpartikel zu messen. Es besteht jedoch Zweifel daran, inwiefern sich diese Technologien auch für die Messurrg von künstlich hergestellten Nanopartikeln verwenden lassen. Aus diesem Grund folcussierten die vorbereitenden Studien für die Arbeitsplatzbeurteilnngen auf die Messung von Pulverri, welche Nan0partike1-Agg10merate enthalten. Sie erlaubten die ldentifikation folgender rnöglicher Quellen von fehlerhaften Messungen an Arbeitsplätzen mit erhöhter Luft-K0nzentrati0n von Nanopartikel Agglomeratenz - Ein Standard SMPS zeigte eine unglaubwürdige bimodale Partikelgrössenverteilung wenn er grössere Nan0par'til<e1Agg10merate gemessen hat. - Grosse Unterschiede im Bereich von Faktor tausend wurden festgestellt zwischen einem Diffusion Size Classiîier und einigen CPC (beziehungsweise dem SMPS). - Die Unterschiede zwischen CPC/SMPS und dem PAS waren geringer, aber abhängig von Grosse oder Typ des gemessenen Pulvers waren sie dennoch in der Grössenordnung von einer guten Grössenordnung. - Spezifische Schwierigkeiten und Unsicherheiten im Bereich von Arbeitsplatzmessungen wurden identitiziert: Hintergrundpartikel können mit Partikeln interagieren die während einem Arbeitsprozess freigesetzt werden. Solche Interaktionen erschweren eine korrekte Einbettung der Hintergrunds-Partikel-Konzentration in die Messdaten. - Elektromotoren produzieren grosse Mengen von Nanopartikeln und können so die Messung der prozessbezogenen Exposition stören. Fazit: Die Umfragen zeigten, dass Nanopartikel bereits Realitàt sind in der Schweizer Industrie und dass einige Unternehmen bereits grosse Mengen davon einsetzen. Die repräsentative Umfrage hat diese explosive Nachricht jedoch etwas moderiert, indem sie aufgezeigt hat, dass die Zahl der Unternehmen in der gesamtschweizerischen Industrie relativ gering ist. In den meisten Branchen (vor allem ausserhalb der Chemischen Industrie) wurden wenig oder keine Anwendungen gefunden, was schliessen last, dass die Einführung dieser neuen Technologie erst am Anfang einer Entwicklung steht. Auch wenn die Zahl der potentiell exponierten Arbeiter immer noch relativ gering ist, so unterstreicht die Studie dennoch die Notwendigkeit von Expositionsmessungen an diesen Arbeitsplätzen. Kenntnisse um die Exposition und das Wissen, wie solche Exposition korrekt zu messen, sind sehr wichtig, vor allem weil die möglichen Auswirkungen auf die Gesundheit noch nicht völlig verstanden sind. Die Evaluation einiger Geräte und Methoden zeigte jedoch, dass hier noch Nachholbedarf herrscht. Bevor grössere Mess-Studien durgefîihrt werden können, müssen die Geräte und Methodem für den Einsatz mit Nanopartikel-Agglomeraten validiert werden.

Prescription footwear for severe injuries of foot and ankle: effect on regularity and symmetry of the gait assessed by trunk accelerometry.

After foot and/or ankle fracture, the restoration of optimal gait symmetry is one of the criteria of recovery. Orthotic insoles and orthopaedic shoes improve gait symmetry and regularity by controlling joint motion and improving alignment. The aim of the present study was to assess the effect of prescription footwear on gait quality by using accelerometers attached to the lower back. Sixteen adult patients with persistent disability after ankle and/or foot fractures performed two 30-s walking trials with and without prescription footwear (insoles and stabilizing shoes). Sixteen control subjects were also tested for comparison. The autocorrelation function was computed from the acceleration signal and the first two dominant periods were assessed (d1 and d2). Two parameters were used: (1) Stride Regularity (SR) which expresses the similarity between strides over time (d2), and (2) Stride Symmetry (SS) a ratio (d1/d2) which expresses the left/right similarity of gait independently of repeatability in the successive movements of each limb. In control subjects, SR and SS were 0.86+/-0.05 (correlation coefficient) and 81+/-10%, respectively. In the patient group, the effect of footwear was significant (SR: 0.88+/-0.06 vs. 0.90+/-0.05, SS: 38+/-23% vs. 46+/-27%). Pain was also significantly reduced (-34%). By using a rapid and low-cost method, we objectively quantified gait quality improvement after footwear intervention, concomitant to pain reduction. Substantial inter-patient variability in the footwear outcome was observed. In conclusion, we believe that trunk accelerometry can be a useful tool in the field of gait rehabilitation.

Effect of External Noise Correlation in Optical Coherence Resonance

Coherence resonance occurring in semiconductor lasers with optical feedback is studied via the Lang-Kobayashi model with external nonwhite noise in the pumping current. The temporal correlation and the amplitude of the noise have a highly relevant influence in the system, leading to an optimal coherent response for suitable values of both the noise amplitude and correlation time. This phenomenon is quantitatively characterized by means of several statistical measures.

Parity violation in Aharonov-Bohm systems: The spontaneous Hall effect

We show how macroscopic manifestations of P (and T) symmetry breaking can arise in a simple system subject to Aharonov-Bohm interactions. Specifically, we study the conductivity of a gas of charged particles moving through a dilute array of flux tubes. The interaction of the electrons with the flux tubes is taken to be of a purely Aharonov-Bohm type. We find that the system exhibits a nonzero transverse conductivity, i.e., a spontaneous Hall effect. This is in contrast to the fact that the cross sections for both scattering and bremsstrahlung (soft-photon emission) of a single electron from a flux tube are invariant under reflections. We argue that the asymmetry in the conductivity coefficients arises from many-body effects. On the other hand, the transverse conductivity has the same dependence on universal constants that appears in the quantum Hall effect, a result that we relate to the validity of the mean-field approximation.

Compared performance of penetrometers and effect of soil water content on penetration resistance measurements

Modern agriculture techniques have a great impact on crops and soil quality, especially by the increased machinery traffic and weight. Several devices have been developed for determining soil properties in the field, aimed at managing compacted areas. Penetrometry is a widely used technique; however, there are several types of penetrometers, which have different action modes that can affect the soil resistance measurement. The objective of this study was to compare the functionality of two penetrometry methods (manual and automated mode) in the field identification of compacted, highly mechanized sugarcane areas, considering the influence of soil water volumetric content (θ) on soil penetration resistance (PR). Three sugarcane fields on a Rhodic Eutrudrox were chosen, under a sequence of harvest systems: one manual harvest (1ManH), one mechanized harvest (1MH) and three mechanized harvests (3MH). The different degrees of mechanization were associated to cumulative compaction processes. An electronic penetrometer was used on PR measurements, so that the rod was introduced into the soil by hand (Manual) and by an electromechanical motor (Auto). The θ was measured in the field with a soil moisture sensor. Results showed an effect of θ on PR measurements and that regression models must be used to correct data before comparing harvesting systems. The rod introduction modes resulted in different mean PR values, where the "Manual" overestimated PR compared to the "Auto" mode at low θ.

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long- and short-wavelength modes of the field. The field model considered consists of a scalar field of mass M with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behavior is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size M-1. This effect makes a substantial contribution to the total decay rate.