Physical States Research Articles

Spin-2 Kaluza-Klein scattering in a stabilized warped background

Scattering amplitudes involving massive spin-2 particles typically grow rapidly with energy. In this paper we demonstrate that the anomalous high-energy growth of the scattering amplitudes cancel for the massive spin-2 Kaluza-Klein modes arising from compactified five-dimensional gravity in a stabilized warped geometry. Generalizing previous work, we show that the two sum rules which enforce the cancellations between the contributions to the scattering amplitudes coming from the exchange of the (massive) radion and those from the exchange of the tower of Goldberger-Wise scalar states (admixtures of the original gravitational and scalar fields of the theory) still persist in the case of the warping which would be required to produce the hierarchy between the weak and Planck scales in a Randall-Sundrum model. We provide an analytic proof of one combination of these generalized scalar sum rules and show how the sum rule depends on the Einstein equations determining the background geometry and the mode-equations and normalization of the tower of physical scalar states. Finally, we provide a consistent and self-contained derivation of the equations governing the physical scalar modes, and we list, in appendixes, the full set of sum rules ensuring proper high-energy growth of all $2\ensuremath{\rightarrow}2$ massive spin-2 scattering amplitudes.

D=5 holomorphic Chern-Simons and the pure spinor superstring

The physical states of D=5 holomorphic Chern-Simons theory correspond to on-shell D=10 open superstring states in the cohomology of q+, where q+ is one of the 16 spacetime supersymmetry generators. Scattering amplitudes of these states can be computed either using the usual Ramond-Neveu-Schwarz (RNS) superstring prescription with N=1 worldsheet supersymmetry, or using a topological ĉ=5 string theory with twisted N=2 worldsheet supersymmetry.It will be argued that the relation between D=5 holomophic Chern-Simons and the RNS superstring is identical to the relation between the pure spinor superstring and the recently constructed B-RNS-GSS superstring which has both N=1 worldsheet supersymmetry and D=10 spacetime supersymmetry. Physical states of the pure spinor superstring correspond to on-shell B-RNS-GSS states which are in the cohomology of λαqα, where λα is a D=10 pure spinor. And scattering amplitudes of these states can be computed either using the full B-RNS-GSS superstring prescription with N=1 worldsheet supersymmetry, or using the pure spinor superstring amplitude prescription with twisted N=2 worldsheet supersymmetry. This should be useful for proving equivalence of the RNS and pure spinor amplitude prescriptions and for clarifying the relation of their multiloop subtleties.

The association between physical behavior, affective states, and contextual factors: Using ambulatory assessment to characterize moderating effects

Introduction
 Physical behavior is a key lifestyle factor in regulating and preventing diseases across the lifespan. Researchers identified affective, cognitive, and contextual factors like weather conditions, as significant contributors in determining if individuals are physically active. However, there is scarce empirical evidence about potential associations between physical behavior and affective states influenced by weather conditions in daily life. Therefore, we investigated the within-subject association between momentary affective states and physical behavior, and weather conditions and physical behavior. Further, we additionally explored if weather conditions moderated the within-subject association between momentary affective states and subsequent physical behavior.
 Methods
 Utilizing ambulatory assessment, 79 participants completed electronic diaries about their affective states (i.e., valence, energetic arousal, and calmness) up to six times a day over five days, and their physical behavior (i.e., physical activity and sedentariness) was simultaneously recorded via accelerometers. Weather conditions (i.e., temperature and precipitation) recorded near participants’ locations served as moderators in the multilevel analyses.
 Results
 We showed, that the association of affective states and physical activity was moderated by temperature. Higher temperatures enhanced the positive effects of valence on physical activity (β = .001, p = .023) and attenuated the negative effects of calmness on physical activity (β = .001, p = .021). Moreover, higher temperatures enhanced the positive effects of valence on reduced sedentary behavior (β = -0.011, p = .043). In addition, we revealed a significant positive association between temperature, as a momentary weather condition, and physical activity (β = 0.025; p = .015). Furthermore, we confirmed earlier findings associating affective states with physical behavior. Increased valence and energetic arousal were positively associated with physical activity (β = 0.007; p < .001), whereas calmness predicted lower levels of physical activity (β = -0.006; p < .001). Higher levels of calmness showed a positive association with sedentary behavior (β = 0.054; p = .003).
 Conclusion
 Moderating effects, such as higher temperatures enhancing the positive effects of valence on PA, provide mechanistic real-life insights as a basis for future health technologies. Just-in-time adaptive interventions (JITAI) offer the possibility to incorporate weather conditions and allow triggering individuals within their preferred contextual condition to promote physical activity. Such personalized real-time systems have recently been promoted by the WHO as most promising.

Allostatic load and physical performance in older adults: Findings from the International Mobility in Aging Study (IMIAS)

ObjectiveThis study aimed to evaluate the association between Allostatic Load (AL) and physical performance scores in older adults from four cities in North and South America. MethodsIn this cross-sectional study, data from 1101 volunteers from three countries (Canada, Brazil, and Colombia) from the International Mobility in Aging Study (IMIAS) were used to evaluate the association between AL index and Short Physical Performance Battery (SPPB) scores. Three multiple linear regression models adjusted by age, Socioeconomic Status (SES), chronic conditions, depression symptoms, and Leganés Cognitive Test (LCT) were developed to estimate the independent association between SPPB and AL. Mediation analysis with 2012 LA data and covariates was performed to access the total, direct, and indirect effects of mediation on SPPB scores from 2016. ResultsAL and SPPB were inversely associated, with older adults with high allostatic load scoring lower on SPPB (β: -0.234, Std: 0.033, p-value: <0.001). Indirect effects were evidenced between age, SES and chronic conditions with AL and SPPB scores. Chronic conditions also had a total effect on SPPB scores and were also mediated by AL. However, indirect effects of depressive symptoms and LCT on SPPB scores mediated by AL were not observed. ConclusionsFindings from this study support that increased AL index determines worse physical performance states after full adjustments. AL has a mediator role between the number of chronic diseases, depressive symptoms, cognitive status and physical performance. Socioeconomic status also influenced physical scores mediated by the AL index.

The effects of sports lessons on emotions in the primary school

Aim&#x0D; Investigate the effect of various intensities of physical activity (PA) on subsequent positive and negative emotions of fourth- to sixth-grade students.&#x0D; Background&#x0D; PA can positively affect children’s mood and emotions and this has previously been suggested as one of the mechanisms by which PA promotes mental health, including cognitive function and well-being (the psychosocial hypothesis, Lubans et al., 2016). In particular, moderate (MPA) and vigorous (VPA) activity have been found to positively affect emotions in children and adolescents (e.g. Bourke et al., 2021; Dunton et al., 2014), with positive emotions more strongly affected by acute PA than negative ones (Bourke et al., 2021).&#x0D; Method&#x0D; Seventy-seven children in fourth to sixth grade from four primary schools in Oxfordshire (United Kingdom) took part in six physical education (PE) lessons. PE lessons varied in their targeted intensity (low, medium, and high) and complexity (each intensity once at low and once at high complexity). During the classroom lesson before and after each physical education lesson, participants reported their emotional state three times via an app on tablets, by rating eight emotions on a 5-point Likert scale.&#x0D; Results&#x0D; Both positive and negative emotions during PE predicted emotions in the classroom after PE. Greater PE lesson enjoyment led to increased positive emotions during PE, and more positive emotions were reported in the classroom after PE when lessons were higher in MPA. VPA led to decreased positive emotions during PE. On the other hand, negative emotions at the end of PE or in the classroom after PE were not affected by moderate (MPA) or vigorous (VPA) PA during PE, or the participants’ enjoyment of the PE lesson. Light PA did not have any significant effect on negative or positive emotions during or after PE. PA intensity did not affect PE lesson enjoyment.&#x0D; Conclusion&#x0D; Negative emotions were not affected by any PA intensity. Positive emotions responded differently depending on PA intensity. Independent of intensity, PE lesson enjoyment strongly improved positive emotions.&#x0D; References&#x0D; Bourke, M., Hilland, T. A., &amp; Craike, M. (2021). A systematic review of the within-person association between physical activity and affect in children’s and adolescents’ daily lives. Psychology of Sport and Exercise, 52, Article 101825. https://doi.org/10.1016/j.psychsport.2020.101825&#x0D; Dunton, G. F., Huh, J., Leventhal, A. M., Riggs, N., Hedeker, D., Spruijt-Metz, D., &amp; Pentz, M. A. (2014). Momentary assessment of affect, physical feeling states, and physical activity in children. Health Psychology, 33(3), 255-263. https://doi.org/10.1037/a0032640&#x0D; Lubans, D., Richards, J., Hillman, C., Faulkner, G., Beauchamp, M., Nilsson, M., Kelly, P., Smith, J., Raine, L., &amp; Biddle, S. (2016). Physical activity for cognitive and mental health in youth: A systematic review of mechanisms. Pediatrics, 138(3), 1642–1656. https://doi.org/10.1542/peds.2016-1642

Integrating Reference Intervals into Chimpanzee Welfare Research

Animal welfare researchers are committed to developing novel approaches to enhance the quality of life of chimpanzees living in professional care. To systematically monitor physical, mental, and emotional states, welfare scientists highlight the importance of integrating non-invasive, animal-based welfare indicators. This study aimed to create species-specific reference intervals for behavioral measures and physiological biomarkers. Specifically, we analyzed data from 40 adult chimpanzees (22 females, 18 males) residing at 16 zoological facilities to generate reference intervals for behavioral states and events, behavioral diversity, fecal glucocorticoid metabolites (GCMs), and fecal immunoglobulin-A (IgA). Comparisons of sex and age using linear regression models revealed significant differences for several behaviors. The proportion of time spent engaged in mutual/multiple social grooming significantly decreased as individuals aged. Furthermore, males spent a higher proportion of time performing aggressive contact behaviors and displaying to other chimpanzees when compared to females. Males also performed sexual examination behaviors at a higher rate than females. Behavioral diversity, fecal GCM, and fecal IgA did not vary by sex or age. In the future, values for individual chimpanzees can be compared to the ranges reported here for particular age/sex classes. Ultimately, animal care professionals can utilize reference intervals to make evidence-based decisions regarding management practices and environmental conditions.

Enhanced the bonding reliability of titanium alloy and CFRTP via interfacial multiple modification: Synergy of physical interlocking and chemical interaction

A novel multiple modification approach including laser texturing, micro-arc oxidation process and silane coupling agent treatment was proposed to optimize the bonding interface. Firstly, laser texturing was fabricated to promote the mechanical interlocking. Secondly, the micro-arc oxidation porous structure was designed to modify its physical structure and chemical states. This promoted the interfacial mechanical interlocking in dual scales including texturing and porous structures. Moreover, the new chemical bonds such as Ti-C and Ti-O were generated at the interface. The bonding strength of TC4/CFRTP was enhanced from 10.23 MPa to 23.41 MPa. Besides, more hydroxyl groups (–OH) were adsorbed inside the optimized structure, and the hydrogen bonds were successfully induced by silane coupling film via the final step. This further enhanced the bonding strength to the maximum of 27.22 MPa. Therefore, the multiple modification approach realized the comprehensive enhancement of mechanical interlocking, chemical bonding and functional groups interaction, which enhanced the bonding reliability by 166% than pretreated case. These results benefit future research in the process optimization to improve the reliability of metal-CFRTP bonding structures.

First extraction of the proton mass radius and scattering length $$\vert\alpha_{\rho^{0}p}\vert$$ from ρ0 photoproduction

As it involves the lightest physical states excited from the vacuum by the vector quark current, near-threshold ρ0 photoproduction is considered a possible way to research the proton radius and the absolute value of the scattering lengths of the ρ0-proton interaction. In this study, under the assumption of a scalar form factor of dipole form, the value of the proton mass radius is calculated as (0.85 ± 0.06) fm by fitting the differential cross section of the γp → ρ0p reaction at near-threshold energy. For light vector meson photoproduction, because the exchange of a scalar quark-antiquark pair is not suppressed and should dominate the scalar gluon exchange, the radius we extract from ρ0 photoproduction is likely to represent the quark radius of the proton. This fact may explain why the value obtained in this study is very near the proton charge radius. Moreover, the absolute value of the ρ0-proton scattering length $$\vert\alpha_{\rho^{0}p}\vert=(0.31 \pm 0.06)$$ fm is obtained for the first time within the vector meson dominance model. This result disobeys the rule that the absolute value of the vector meson and proton scattering length $$\vert\alpha_{V_{p}}\vert$$ increases with the meson’s mass, which can be attributed to treating the ρ0 meson as a point in the analysis. These results provide useful theoretical information for an in-depth understanding of proton structure and the proton-vector meson interaction.

Nanoscopy on drug-encapsulating nanosystems by phasor-based fluorescence lifetime analysis.

Understanding the supramolecular organization of active compounds (drugs) encapsulated within standard formulations is becoming increasingly important in nanomedicine. In fact, the synthetic identity of a drug-encapsulating nanosystem is supposed to change throughout its journey, from administration to final fate within the target tissue/cell. Here we addressed this issue by exploiting phasor-based fluorescence lifetime imaging (FLIM) of a drug intrinsic fluorescence signal. As case-study, we selected Irinotecan (CPT-11), a chemotherapy medication used to treat colon cancer, small lung cancer and pancreatic cancer, and focused on its liposomal formulation Onivyde®, launched in 2015 as an orphan drug for the treatment of metastatic ductal adenocarcinoma (mPDAC). After measuring the FLIM signature of the drug's individual physical states, we extracted the fractional intensities of each coexisting physical state of the active principle within the nanoparticle. Our analysis was boosted by means of dedicated custom algorithms based on preliminary data processing and multi-dimensional histogram inference to identify regions of interest in the phasor plot. Whereas, in the case of biological samples, we achieved autonomous cell segmentation by means of computer vision algorithms. Onivyde® in commercial vials was found to coexist in multiple physical states (i.e. gelated/precipitated, free and membrane-associated) and undergo extensive leakage in media mimicking complex biological environments. Moreover, we identified multiple mechanism of cellular uptake and were able to investigate subcellular localization and supramolecular organization of irinotecan in a model of pancreatic cells. In conclusion, we believe that Phasor-FLIM represents a useful platform to quantitatively address the synthetic identity of encapsulated fluorescent drugs, both in cuvette and cellular environments. In this context, we envision many potential applications ranging from batch-to-batch analysis, at the production level, to drug development optimization.

Emotions in ancient Egypt—An overview

AbstractThe aim of the article is to present essential aspects of five emotions (joy, fear, love, sadness, anger) on the basis of written sources from ancient Egypt. Through selective analyses of the Egyptian emotion vocabulary, including metaphors and descriptions of physical states and reactions, some elementary concepts will be explained. In addition, it is a concern to point out some of the difficulties that can be associated with the investigation of emotions in ancient Egyptian texts. Therefore, brief references are given to current Egyptological studies that have been devoted to the topic adopting new methods.

Industrial Biotechnology Conservation Processes: Similarities with Natural Long-Term Preservation of Biological Organisms

Cryopreservation and lyophilization processes are widely used for conservation purposes in the pharmaceutical, biotechnological, and food industries or in medical transplantation. Such processes deal with extremely low temperatures (e.g., -196 °C) and multiple physical states of water, a universal and essential molecule for many biological lifeforms. This study firstly considers the controlled laboratory/industrial artificial conditions used to favor specific water phase transitions during cellular material cryopreservation and lyophilization under the Swiss progenitor cell transplantation program. Both biotechnological tools are successfully used for the long-term storage of biological samples and products, with reversible quasi-arrest of metabolic activities (e.g., cryogenic storage in liquid nitrogen). Secondly, similarities are outlined between such artificial localized environment modifications and some natural ecological niches known to favor metabolic rate modifications (e.g., cryptobiosis) in biological organisms. Specifically, examples of survival to extreme physical parameters by small multi-cellular animals (e.g., tardigrades) are discussed, opening further considerations about the possibility to reversibly slow or temporarily arrest the metabolic activity rates of defined complex organisms in controlled conditions. Key examples of biological organism adaptation capabilities to extreme environmental parameters finally enabled a discussion about the emergence of early primordial biological lifeforms, from natural biotechnology and evolutionary points of view. Overall, the provided examples/similarities confirm the interest in further transposing natural processes and phenomena to controlled laboratory settings with the ultimate goal of gaining better control and modulation capacities over the metabolic activities of complex biological organisms.

Exploring wettability difference-driven wetting by utilizing electrospun chimeric Janus microfiber comprising cellulose acetate and polyvinylpyrrolidone

In exploring the difference in the wettability of fibers with various structures, three inner constructions of fibers, namely, uniaxial, Janus and chimeric Janus, have been fabricated by electrospinning. In electrospun fibers, polyvinyl pyrrolidone and cellulose acetate were used as a polymer matrix and ketoprofen was used as a model drug. Morphologies and inner structures were respectively investigated by scanning electron microscopy (SEM) and Transmission electron microscopy (TEM). Physical states and compatibilities of materials were detected by X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR). Water contact angle (WCA) tests were conducted to determine the difference between wettability and wetting time among assorted fiber membranes. Results showed that the wettability gradient could drive water movement and wetting, which resulted in the rapid decrease of the WCA, to prepare Janus and chimeric Janus fiber membranes compared with uniaxial fiber membranes. Otherwise, in vitro drug release experiments were carried out and four fitting models were applied in matching release profiles. The results showed that electrospun fiber membranes belonged to sustained-release systems and such membranes were influenced by drug diffusion and backbone corrosion effects. In this study, whether electrospun multilayer Janus fibers could affect wettability and drug release was investigated.

Recent Advance in Cortisol Immunosensing Technologies and Devices

Well known as the “stress hormone”, cortisol plays an indispensable role in life activities. In the past few decades, accurate information about the intracorporal level of cortisol has been proven to be an important and effective indicator for evaluating physical and mental states and diagnosing a series of pressure-induced diseases. Hence, various rapid and efficient cortisol sensing technologies with high sensitivity and selectivity and low detection limit have been developed. This review examines most recent works and progress in cortisol detection via immunoassay, highlighting the construction of sensitive sensor systems. We aimed to provide a comprehensive description in the aspects of general optical and electrochemical detection methods, novel immunosensing systems, and advanced portable and wearable devices. Outlooks and suggestions for the development of continuous and real-time monitoring techniques and devices were finally provided.

Laboratory test and prediction model of dynamic resilient modulus of carbonaceous mudstone coarse-grained soil

Carbonaceous mudstone is widely distributed in southwest China. With the rapid development of transportation construction in this region, the use of carbonaceous mudstone for subgrade filling has good economic and environmental benefits. At present, studies on the dynamic characteristics of carbonaceous mudstone coarse-grained soil are few. The shape characteristics of mudstone particles and the compaction characteristics of subgrade fillings with different grades are analyzed then dynamic triaxial tests are conducted to explore the variation of the dynamic resilient modulus MR of carbonaceous mudstone coarse-grained soil under different stresses and physical states. The influence of different gradation, confining pressure σ3, dynamic deviatoric stress σd, moisture content w, and degree of compaction K on MR of carbonaceous mudstone coarse-grained soil was studied. Results indicate that the particle shape index of carbonaceous mudstone is insensitive to particle size. With the increase in the gradation parameter D, the optimal moisture content wopt of the sample increases, whereas the maximum dry density ρdmax initially increases, and then decreases. MR is positively correlated with σ3 and K, but negatively correlated with σd and w. The decrease of MR caused by w decreases gradually with the increase of D. When w≤ 1.1 *wopt, the increase in D reduces MR, but when w= 1.2 *wopt, the trend changes to a positive correlation between MR and D. Carbonaceous mudstone subgrade filling can be used for the highway with light or medium traffic load grade. The recommended gradation parameter D ranges from 2.43 to 2.63. A resilient modulus prediction model considering the influence of gradation, stress state, moisture content, and physical state is proposed and its rationality is verified. The research results can provide reference for the design of carbonaceous mudstone coarse-grained soil subgrade.

Spinor representation of the Hamiltonian constraint in 3D loop quantum gravity with a nonzero cosmological constant

We develop in a companion paper the kinematics of three-dimensional loop quantum gravity in Euclidean signature and with a negative cosmological constant, focusing in particular on the spinorial representation that is well known at zero cosmological constant. In this paper, we put this formalism to the test by quantizing the Hamiltonian constraint on the dual of a triangulation. The Hamiltonian constraints are obtained by projecting the flatness constraints onto spinors, as done in the flat case by the first author and Livine. Quantization then relies on $q$-deformed spinors. The quantum Hamiltonian constraint acts in the $q$-deformed spin network basis as difference equations on physical states, which are thus the Wheeler-DeWitt equations in this framework. Moreover, we study how physical states transform under Pachner moves of the canonical surface. We find that those transformations are in fact $q$ deformations of the transition amplitudes of the flat case as found by Noui and Perez. Our quantum Hamiltonian constraints, therefore, build a Turaev-Viro model at real $q$.

Silicone matrices for controlled dexamethasone release: toward a better understanding of the underlying mass transport mechanisms.

Dexamethasone-loaded silicone matrices offer an interesting potential as innovative drug delivery systems, e.g. for the treatment of inner ear diseases or for pacemakers. Generally, very long drug release periods are targeted: several years/decades. This renders the development and optimization of novel drug products cumbersome: experimental feedback on the impact of the device design is obtained very slowly. A better understanding of the underlying mass transport mechanisms can help facilitating research in this field. A variety of silicone films were prepared in this study, loaded with amorphous or crystalline dexamethasone. Different polymorphic drug forms were investigated, the film thickness was altered and the drug optionally partially/completely exchanged by much more water-soluble dexamethasone 'phosphate'. Drug release studies in artificial perilymph, scanning electron microscopy, optical microscopy, differential scanning calorimetry, X-ray diffraction and Raman imaging were used to elucidate the physical states of the drugs and polymer, and of the systems' structure as well as dynamic changes thereof upon exposure to the release medium. Dexamethasone particles were initially homogeneously distributed throughout the systems. The hydrophobicity of the matrix former very much limits the amounts of water penetrating into the system, resulting in only partial drug dissolution. The mobile drug molecules diffuse out into the surrounding environment, due to concentration gradients. Interestingly, Raman imaging revealed that even very thin silicone layers (<20 µm) can effectively trap the drug for prolonged periods of time. The physical state of the drug (amorphous, crystalline) did not affect the resulting drug release kinetics to a noteworthy extent.

Neural Correlates of Cue-Evoked Synchronous Fear Responses

Visiting a haunted house with friends is a rite of passage among teenagers. Interestingly, researchers find increased arousal and attentiveness to fear responses in response to threat when in the presence of friends (1). Increased fear responses within a group are an example of emotional contagion, considered to be a primitive form of empathy (2). Emotional contagion is defined as the automatic mimicry of the physical and emotional states of another individual. Emotional contagion of both positive and negative valence is used in every social interaction and increases unconscious behavioral synchrony (2).

An energy-based model for the generation of excess pore water pressure in saturated coral sand

A series of undrained cyclic shear tests was carried out on saturated coral sands, with different initial physical states, as they were subjected to rotations of 90° in the paths of cyclic stress with various initial orientations under isotropic conditions. An important finding is that the cumulative dissipated energy required for liquefaction (W s) was significantly affected by their fines content (FC), relative density (D r), and effective stress of consolidation ( p ′ 0 ), but was independent of the conditions of cyclic loading. W s increased significantly with the increase in p ′ 0 . When FC was less than the threshold fines content, W s increased with FC and decreased with an increase in D r. The equivalent intergranular void ratio (e*) was introduced to reflect the effects of FC, physical states of the particles, and inter-particle contact on the physical properties of coral sand. The results revealed a unique relationship between e* and W s at p ′ 0 = 100 kPa. Furthermore, the unified model of the relation between the normalized cumulative dissipated energy and the ratio of excess pore water pressure (EPWP) followed an arc-tangent function. This model can be used to characterize the generation of EPWP with the cumulative dissipated energy of fine-grained sand under isotropic consolidation conditions.

Stigmatized experience is associated with exacerbated pain perception in depressed patients

Patients with depression not only have to cope with depressive and physical symptoms but also face stigmatization due to mental illness. Pain is a clinical symptom of many patients with depression. However, it is unclear whether stigmatized experience associated with mental illness directly affects depressed patients' pain perception. Here, using the event reflection task, Study 1 (N = 95) examined whether stigmatized experiences due to depression would affect patients' self-reported pain assessment. Study 2 (N = 43) further employed thermal stimuli at different intensities to examine whether stigmatization would affect patients' evoked pain. We found that patients with depression who experienced stigmatization based on mental illness reported higher pain catastrophizing and performed increased pain perception for noxious stimuli than those who did not. Our studies provide first-hand experimental evidence of the effect of stigmatized experiences on depressed patients’ pain perception. The findings contribute insights for improving clinical treatment, suggesting that interventions should minimize stigmatization associated with mental illness to help patients maintain healthier physical and psychological states.

Toeplitz density operators and their separability properties

Toeplitz operators (also called localization operators) are a generalization of the well-known anti-Wick pseudodifferential operators studied by Berezin and Shubin. When a Toeplitz operator is positive semi-definite and has trace one we call it a density Toeplitz operator. Such operators represent physical states in quantum mechanics. In the present paper we study several aspects of Toeplitz operators when their symbols belong to some well-known functional spaces (e.g. the Feichtinger algebra) and discuss (tentatively) their separability properties with an emphasis on the Gaussian case.